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All Textbook Solutions for PREALGEBRA

In the following exercises, identify all sets of like terms. 6z, 3w2, 1, 6z2, 4z, w2In the following exercises, identify all sets of like terms. 9a, a2, 16ab, 16b2, 4ab, 9b2In the following exercises, identify all sets of like terms. 3, 25r2, 10s, 10r, 4r2, 3sIn the following exercises, simplify the given expression by combining like terms. 10x+3xIn the following exercises, simplify the given expression by combining like terms. 15x+4xIn the following exercises, simplify the given expression by combining like terms. 17a+9aIn the following exercises, simplify the given expression by combining like terms. 18z+9zIn the following exercises, simplify the given expression by combining like terms. 4c+2c+cIn the following exercises, simplify the given expression by combining like terms. 6y+4y+yIn the following exercises, simplify the given expression by combining like terms. 9x+3x+8In the following exercises, simplify the given expression by combining like terms. 8a+5a+9In the following exercises, simplify the given expression by combining like terms. 7u+2+3u+1In the following exercises, simplify the given expression by combining like terms. 8d+6+2d+5In the following exercises, simplify the given expression by combining like terms. 7p+6+5p+4In the following exercises, simplify the given expression by combining like terms. 8x+7+4x5In the following exercises, simplify the given expression by combining like terms. 10a+7+5a2+7a4In the following exercises, simplify the given expression by combining like terms. 7c+4+6c3+9c1In the following exercises, simplify the given expression by combining like terms. 3x2+12x+11+14x2+8x+5In the following exercises, simplify the given expression by combining like terms. 5b2+9b+10+2b2+3b4In the following exercises, translate the given word phrase into an algebraic expression. The sum of 8 and 12In the following exercises, translate the given word phrase into an algebraic expression. The sum of 9 and 1In the following exercises, translate the given word phrase into an algebraic expression. The difference of 14 and 9In the following exercises, translate the given word phrase into an algebraic expression. 8 less than 19In the following exercises, translate the given word phrase into an algebraic expression. The product of 9 and 7In the following exercises, translate the given word phrase into an algebraic expression. The product of 8 and 7In the following exercises, translate the given word phrase into an algebraic expression. The qoutiendt of 36 and 9In the following exercises, translate the given word phrase into an algebraic expression. The quotient of 42 and 7In the following exercises, translate the given word phrase into an algebraic expression. The difference of xand 4In the following exercises, translate the given word phrase into an algebraic expression. 3 less than xIn the following exercises, translate the given word phrase into an algebraic expression. The product of 6 and yIn the following exercises, translate the given word phrase into an algebraic expression. The product of 9 and yIn the following exercises, translate the given word phrase into an algebraic expression. The sum of 8xand 3xIn the following exercises, translate the given word phrase into an algebraic expression. The sum of 13xand 3xIn the following exercises, translate the given word phrase into an algebraic expression. The quotient of yand 3In the following exercises, translate the given word phrase into an algebraic expression. The quotient of yand 8In the following exercises, translate the given word phrase into an algebraic expression. Eight times the difference of yand nineIn the following exercises, translate the given word phrase into an algebraic expression. Seven times the difference of yand oneIn the following exercises, translate the given word phrase into an algebraic expression. Five times the sum of xand yIn the following exercises, translate the given word phrase into an algebraic expression. Nine times five less than twice xIn the following exercises, translate, write an algebraic expression. Adele bought a skirt and a blouse. The cost 15more than the blouse. Let brepresent the cost of the blouse. Write an expression for the cost of the skirt.In the following exercises, write an algebraic expression. Eric has rock and classical CDs in his car. The number of rock CDs is 3more than the number of classical CDs. Let crepresent the number of classical CDs. Write an expression for the number of rock CDs.In the following exercises, write an algebraic expression. The number of girls in a second-grade class is 4less than the number of boys. Let b represent the number of boys. Write an expression for the number of girls.In the following exercises, write an algebraic expression. Marcella has 6fewer male cousins than female cousins. Let frepresent the number of female cousins. Write an expression for the number of boy cousins.In the following exercises, write an algebraic expression. Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let nrepresent the number of nickels. Write an expression for the number of pennies.In the following exercises, write an algebraic expression. Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let trepresent the number of tens. Write an expression for the number of fives.In the following exercises, write an algebraic expression to solve the problem 143. Car insurance Justin’s car insurance has a $750 deductible per incident. This means that he pays $750 and his insurance company will pay all costs beyond $750. If Justin files a claim for $2,100. how much will he pay, and how much will his insurance company pay?In the following exercises, write an algebraic expression to solve the problem 144. Home insurance Pam and Armando’s home insurance has a $2,500 deductible per incident. This means that they pay $2,500 and their insurance company will pay all costs beyond $2,500. If Pam and Armando file a claim for $19.400. how much will they pay, and how much will their insurance company pay?Explain why “the sum of xand y” is the same as “the sum of yand x,” but “the difference of xand y” is not the same as “the difference of yand x.” Try substituting two random numbers for x and yto help you explain.Explain the difference between “4 times the sum of xand y” and “the sum of 4 times xand y.”TRY IT:: 2.55 Isx= 3 a solution of 4x7=16?TRYIT::2.56 Isx=2a solution of 6x2=10?TRY IT:: 257 Is y = 3 a solution of 9y2=8y+1 ?TRY IT:: 2.58 Is y = 4 a solution of 5y3=3y+5 ?TRY IT 2.59 Write the equation modeled by the envelopes and counters, and then solve the equation:RY IT:: 2.60 Write the equation modeled by the envelopes and counters, and then solve the equation:TRY fl :: 2.61 Solve: x+6=19TRY IT :: 2.62 Solve: x+9=14TRY IT :: 2.63 Solve: 95=y+67TRY IT :: 2.64 Solve: 91=y+45TRY IT :: 2.65 Solve: x9=13TRY IT :: 2.66 Solve: y1=3TRY IT :: 2.67 Solve: 19=a18TRY IT :: 2.68 Solve: 27=n14TRY IT :: 2.69 Translate the sentence into an algebraic equation: The sum of 7 and 6 gives 13.TRY IT :: 2.70 Translate the sentence into an algebraic equation: The sum of 8 and 6 is 14.TRY IT :: 2.71 Translate the sentence into an algebraic equation: The product of 6 and 9 is 54.TRY IT :: 2.72 Translate the sentence into an algebraic equation: The product of 21 and 3 gives 63.TRY IT :: 2.73 Translate the given sentence into an algebraic equation: Twice the difference of xand 5 gives 30.TRY IT :: 2.74 Translate the given sentence into an algebraic equation: Twice the difference of yand 4 gives 16.TRY IT :: 2.75 Translate and solve: Seven more than xis equal to 37.TRY IT :: 2.76 Translate and salve: Eleven more than yis equal to 28.TRY IT :: 2.77 Translate and solve: The difference of zand 17 is equal to 37.TRY IT :: 2.78 Translate and solve: The difference of xand 19 is equal to 45.In the following exercises, determine whether each given value is a solution to the equation. x+13=21 (a) x=8(b) x=34âIn the following exercises, determine whether each given value is a solution to the equation. y+18=28 (a) y=7(b) y=43In the following exercises, determine whether each given value is a solution to the equation. m4=13 (a) m=9(b) m=17In the following exercises, determine whether each given value is a solution to the equation. n9=6 (a) n=3(b) n=15In the following exercises, determine whether each given value is a solution to the equation. 3p+6=15 (a) p=3(b) p=7In the following exercises, determine whether each given value is a solution to the equation 8q+4=20 (a) q=2(b) q=3In the following exercises, determine whether each given value is a solution to the equation 18d9=27 (a) d=1(b) d=2In the following exercises, determine whether each given value is a solution to the equation 24f12=60 (a) f=2(b) f=3In the following exercises, determine whether each given value is a solution to the equation 8u4=4u+40 (a) u=3(b) u=11In the following exercises, determine whether each given value is a solution to the equation 7v3=4v+36 (a) v=3(b) v=11In the following exercises, determine whether each given value is a solution to the equation 20h5=15h+35 (a) h=6(b) h=8In the following exercises, determine whether each given value is a solution to the equation 18k3=12k+33 (a) k=1(b) k=6In the following exercises. Write the equation modeled by the envelopes and counters and then solve using the subtraction property of equalityIn the following exercises. Write the equation modeled by the envelopes and counters and then solve using the subtraction property of equalityIn the following exercises. Write the equation modeled by the envelopes and counters and then solve using the subtraction property of equalityIn the following exercises. Write the equation modeled by the envelopes and counters and then solve using the subtraction property of equalityIn the following exercises, solve each equation using the subtraction property of equality. a+2=18In the following exercises, solve each equation using the subtraction property of equality. b+5=13In the following exercises, solve each equation using the subtraction property of equality. p+18=23In the following exercises, solve each equation using the subtraction property of equality. q+14=31In the following exercises, solve each equation using the subtraction property of equality. r+76=100In the following exercises, solve each equation using the subtraction property of equality. s+62=95In the following exercises, solve each equation using the subtraction property of equality. 16=x+9In the following exercises, solve each equation using the subtraction property of equality. 17=y+6In the following exercises, solve each equation using the subtraction property of equality. 93=p+24In the following exercises, solve each equation using the subtraction property of equality. 116=q+79In the following exercises, solve each equation using the subtraction property of equality. 465=d+398In the following exercises, solve each equation using the subtraction property of equality. 932=c+641In the following exercises, solve each equation using the subtraction property of equality. y3=19In the following exercises, solve each equation using the addition property of equality. x4=12In the following exercises, solve each equation using the addition property of equality. u6=24In the following exercises, solve each equation using the addition property of equality. v7=35In the following exercises, solve each equation using the addition property of equality. f55=123In the following exercises, solve each equation using the addition property of equality. g39=117In the following exercises, solve each equation using the addition property of equality. 19=n13In the following exercises, solve each equation using the addition property of equality. 18=m15In the following exercises, solve each equation using the addition property of equality. 10=p38In the following exercises, solve each equation using the addition property of equality. 18=q72In the following exercises, solve each equation using the addition property of equality. 268=y199In the following exercises, solve each equation using the addition property of equality. 204=z149In the following exercises, solve each equation using the addition property of equality. The sum of 8 and 9 is equal to 17.In the following exercises, translate the given sentence into an algebraic equation. The sum of 7 and is equal to 16.In the following exercises, translate the given sentence into an algebraic equation. The difference of 23 and 19 is equal to 4.In the following exercises, translate the given sentence into an algebraic equation. The difference of 29 and 12 is equal to 17.In the following exercises, translate the given sentence into an algebraic equation. The product of 3 and 9 is equal to 27.In the following exercises, translate the given sentence into an algebraic equation. The product of 6 and 8 is equal to 48.In the following exercises, translate the given sentence into an algebraic equation. The quotient of 54 and 6 is equal to 9.In the following exercises, translate the given sentence into an algebraic equation. The quotient of 42 and 7 is equal to 6.In the following exercises, translate the given sentence into an algebraic equation. Twice the difference of nand 10 gives 52.In the following exercises, translate the given sentence into an algebraic equation. Twice the difference of mand 14 gives 64.In the following exercises, translate the given sentence into an algebraic equation. The sum of three times yand 10 is 100.In the following exercises, translate the given sentence into an algebraic equation. The sum of eight times xand 4 is 68.In the following exercises, translate the given sentence into an algebraic equation and then solve it Five more than pis equal to 21.In the following exercises, translate the given sentence into an algebraic equation and then solve it Nine more than qis equal to 40.In the following exercises, translate the given sentence into an algebraic equation and then solve it The sum of rand 18 is 73.In the following exercises, translate the given sentence into an algebraic equation and then solve it The sum of sand 13 is 68.In the following exercises, translate the given sentence into an algebraic equation and then solve it The difference of dand 30 is equal to 52.In the following exercises, translate the given sentence into an algebraic equation and then solve it The difference of cand 25 is equal to 75.In the following exercises, translate the given sentence into an algebraic equation and then solve it less than uis 89.In the following exercises, translate the given sentence into an algebraic equation and then solve it less than w is 56.In the following exercises, translate the given sentence into an algebraic equation and then solve it less than cgives 799.In the following exercises, translate the given sentence into an algebraic equation and then solve it less than dgives 850.Insurance Vince’s car insurance has a $500 deductible. Find the amount the insurance company will pay, p,for an $1800 claim by solving the equation 500 + p= 1800.Insurance Marta’s homeowner’s insurance policy has a $750 deductible. The insurance company paid $5800 to repair damages caused by a storm. Find the total cost of the storm damage, d,by solving the equation d—750 = 5800.Sale purchase Arthur bought a suit that was on sale for $120 off. He paid $340 for the suit. Find the Original price, p,of the suit by solving the equation p120=340.Sale purchase Rita bought a sofa that was on sale for $1299. She paid a total of $1409, including sales tax. Find the amount of the sales tax, t,by solving the equation 1299+t=1400.Is x=1a solution to the equation 8x2=166x?How do you know?Write the equation y5=21in words. Then make up a word problem for this equation.TRY IT :: 2.79 Determine whether each number is a multiple of 2: 678 21,493TRY IT :: 280 Determine whether each number is a multiple of 2: 979 17,780TRY lT :: 2.81 Determine whether each number is a multiple of 5. 675 1,578TRY IT :: 282 determine whether each number is a multiple of 5. (a) 421 (b) 2,690TRY IT :: Determine whether each number is a multiple of 10: (a) 17 (b) 3,540TRY IT :: 2.84 Determine whether each number is a multiple of 10: (a) 110 (b) 7,595TRY IT :: 2.85 Determine whether each number is a multiple of 3: (a) 954 (b) 3,742TRY IT :: 286 Determine whether each number is a multiple of 3: (a) 643 (b) 8,379TRY IT :: 2.87 Determine whether the given number is divisible by 2, 3, 5, and 10.TRY IT :: 2.88 Determine whether the given number is divisible by 2, 3, 5, and 10.TRY IT :: 2.89 Determine whether the given number is divisible by 2, 3, 5, and 10.TRY IT :: 2.90 Determine whether the given number is divisible by 2, 3, 5, and 10.TRY IT :: 2.91 Find all the factors of the given number:TRY IT :: 2.92 Find all the factors of the given number:TRY IT :: 2.93 Identify the number as prime or composite:TRY IT :: 2.94 Identify the number as prime or composite:In the following exercises, list all the multiples less than 50 for the given number. 215. 2In the following exercises, list all the multiples less than 50 for the given number. 3In the following exercises, list all the multiples less than 50 for the given number. 4In the following exercises, list all the multiples less than 50 for the given number. 5In the following exercises, list all the multiples less than 50 for the given number. 6In the following exercises, list all the multiples less than 50 for the given number. 7In the following exercises, list all the multiples less than 50 for the given number. 8In the following exercises, list all the multiples less than 50 for the given number. 9In the following exercises, list all the multiples less than 50 for the given number. 10In the following exercises, list all the multiples less than 50 for the given number. 12In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 84In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 96In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3,4, 5, 6 and 10. 75In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10.In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 168In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5,6 and 10.In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5,6 and 10. 900In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 800In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 896In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 942In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 375In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 750In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 350In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 550In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 1430In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10.In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6 and 10. 22,335In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 4, 5, 6, and 10. 39,075In the following exercises, find all the factors of the given number.In the following exercises, find all the factors of the given number. 42In the following exercises, find all the factors of the given number. 60In the following exercises, find all the factors of the given number. 48In the following exercises, find all the factors of the given number. 144In the following exercises, find all the factors of the given number. 200In the following exercises, find all the factors of the given number. 588In the following exercises, find all the factors of the given number. 576In the following exercises, determine if the given number is prime or composite. 43In the following exercises, determine if the given number is prime or composite. 67In the following exercises, determine if the given number is prime or composite. 39In the following exercises, determine if the given number is prime or composite. 53In the following exercises, determine if the given number is prime or composite. 71In the following exercises, determine if the given number is prime or composite. 119In the following exercises, determine if the given number is prime or composite. 481In the following exercises, determine if the given number is prime or composite. 221In the following exercises, determine if the given number is prime or composite. 209In the following exercises, determine if the given number is prime or composite. 359In the following exercises, determine if the given number is prime or composite. 667In the following exercises, determine if the given number is prime or composite. 1771Banking. Frank’s grandmother gave him $100 at his high school graduation. Instead of spending it, Frank opened a bank account. Every week, he added $15 to the account. The table shows how much money Frank had put in the account by the end of each week. Complete the table by filling in the blanks.Banking In March, Gina opened a Christmas club savings account at her bank. She deposited $75 to open the account. Every week, she added $20 to the account. The table shows how much money Gina had put in the account by the end of each week. Complete the table by filling in the blanks.If a number is divisible by 2 and by 3, why is it also divisible by 6?What is the difference between prime numbers and composite numbers?TRY IT :: 2.95 Find the prime factorization using the factor tree method: 80TRY IT :: 2.96 Find the prime factorization using the factor tree method: 60TRY IT :: 2.97 Find the prime factorization using the factor tree method: 126TRY IT :: 2.98 Find the prime factorization using the factor tree method: 294TRY IT :: 2.99 Find the prime factorization using the ladder method: 80TRY IT :: 2.100 Find the prime factorization using the ladder method: 60TRY IT :: 2.101 Find the prime factorization using the ladder method. 126TRY IT :: 2.102 Find the prime factorization using the ladder method. 294TRY IT :: 2.103 Find the least common multiple (LCM) of the given numbers: 9 and 12TRY IT :: 2.104 Find the least common multiple (LCM) of the given numbers: 18 and 24TRY IT :: 2.105 Find the LCM using the prime factors method. 15 and 20TRY IT :: 2.106 Find the LCM using the prime factors method. 15 and 35TRY IT :: 2.107 Find the LCM using the prime factors method: 55, 88TRY IT :: 2.108 Find the LCM using the prime factors method: 60, 72In the following exercises, find the prime factorization of each number using the factor tree method.In the following exercises, find the prime factorization of each number using the factor tree method. 78In the following exercises, find the prime factorization of each number using the factor tree method. 132In the following exercises, find the prime factorization of each number using the factor tree method. 455In the following exercises, find the prime factorization of each number using the factor tree method. 693In the following exercises, find the prime factorization of each number using the factor tree method. 420In the following exercises, find the prime factorization of each number using the factor tree method. 115In the following exercises, find the prime factorization of each number using the factor tree method. 225In the following exercises, find the prime factorization of each number using the factor tree method.In the following exercises, find the prime factorization of each number using the factor tree method.In the following exercises, find the prime factorization of each number using the ladder method. 56In the following exercises, find the prime factorization of each number using the factor ladder method. 72In the following exercises, find the prime factorization of each number using the ladder method. 168In the following exercises, find the prime factorization of each number using the ladder method. 252In the following exercises, find the prime factorization of each number using the ladder method. 391In the following exercises, find the prime factorization of each number using the ladder method. 400In the following exercises, find the prime factorization of each number using the ladder method.In the following exercises, find the prime factorization of each number using the ladder method. 627In the following exercises, find the prime factorization of each number using the ladder method.In the following exercises, find the prime factorization of each number using the ladder method.In the following exercises, find the prime factorization of each number using any method. 150In the following exercises, find the prime factorization of each number using any method. 180In the following exercises, find the prime factorization of each number any method. 525In the following exercises, find the prime factorization of each number using any method. 444In the following exercises, find the prime factorization of each number any method. 36In the following exercises, find the prime factorization of each number any method. 50In the following exercises, find the prime factorization of each number using any method. 350In the following exercises, find the prime factorization of each number using any method. 144In the following exercises, find the least common multiple (LCM) by listing multiples.In the following exercises, find the least common multiple (LCM) by listing multiples. 4, 3In the following exercises, find the least common multiple (LCM) by listing multiples. 6, 15In the following exercises, find the least common multiple (LCM) by listing multiples. 12, 16In the following exercises, find the least common multiple (LCM) by listing multiples. 30, 40In the following exercises, find the least common multiple (LCM) by listing multiples. 20, 30In the following exercises, find the least common multiple (LCM) by listing multiples. 60, 75In the following exercises, find the least common multiple (LCM) by listing multiples. 302. 44 , 55In the following exercises, find the least common multiple (LCM) by using the prime factors method.In the following exercises, find the least common multiple (LCM) by using the prime factors method.In the following exercises, find the least common multiple (LCM) by using the prime factors method. 24,30In the following exercises, find the least common multiple (LCM) by using the prime factors method.In the following exercises, find the least common multiple (LCM) by using the prime factors method.In the following exercises, find the least common multiple (LCM) by using the prime factors method.In the following exercises, find the least common multiple (LCM) using any method. 6, 21In the following exercises, find the least common multiple (LCM) using any method. 9, 15In the following exercises, find the least common multiple (LCM) using any method. 24, 30In the following exercises, find the least common multiple (LCM) using any method. 32, 40Grocery shopping Hot dogs are sold in packages of ten, but hot dog buns come in packs of eight. What is the smallest number of hot dogs and buns that can be purchased if you want to have the same number of hot dogs and buns? (Hint: it is the LCM!)Grocery shopping Paper plates are sold in packages of 12 and party cups come in packs of 8. What is the smallest number of plates and cups you can purchase if you want to have the same number of each? (Hint: it is the LCM!)Do you prefer to find the prime factorization of a Composite number by using the factor tree method or the ladder method? Why?Do you prefer to find the LCM by listing multiples or by using the prime factors method? Why?In the following exercises, translate from algebra to English. 3.8In the following exercises, translate from algebra to English. 12xIn the following exercises, translate from algebra to English. 246In the following exercises, translate from algebra to English. 9+2aIn the following exercises, translate from algebra to English. 5047In the following exercises, translate from algebra to English. 3y15In the following exercises, translate from algebra to English. n+4=13In the following exercises, translate from algebra to English. 32k=7In the following exercises, determine if each is an expression or equation. 5+u=84In the following exercises, determine if each is an expression or equation. 366sIn the following exercises, determine if each is an expression or equation. 4y11In the following exercises, determine if each is an expression or equation. 10x=120In the following exercises, write in exponential form. 222In the following exercises, write in exponential form. aaaaaIn the following exercises, write in exponential form. xxxxxxIn the following exercises, write in exponential form. 101010In the following exercises, write in expanded form. 84In the following exercises, write in expanded form. 36In the following exercises, write in expanded form. y5In the following exercises, write in expanded form. n4In the following exercises, simplify each expression. 34In the following exercises, simplify each expression. 106In the following exercises, simplify each expression. 27In the following exercises, simplify each expression. 340. 43In the following exercises, simplify. 10+25In the following exercises, simplify. (10+2)5In the following exercises, simplify. (30+6)2