Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![Step 2:
Step 3:
5.
(2x + 1)(x-4) ≥ 0
(2x +1)(x-4)= 0
2x + 1 = 0,
x-2
2
2x = 1,
x = - ¹1/₂
x²-1
x²-9
20
x-4=0
x=4
Factorize
Find the zeros of the equation
The intervals (-∞, - ¹1/2] U [4, ∞) satisfy the inequality 2x² - 7x2 4.
Solve and graph the following inequalities. (Student problems)
1. x25x26
2. x24x5<0
3. x³-4x ≥ 0
4. 1
3
X
++
-21-
-
c) 7-2x = 5-x
d) 2x + 7 6-3x = 8
+
b) Represent U, A, B, and C on a Venn diagram.
c) Find BUC and A n (BUC)
x+1 x +3
- 1¹/2
+
Written Exercise 1
1. Given that U is a universal set that contains all whole numbers less than 10
and A and B are subset of U. Suppose A (all factors of 18), B-{natural
numbers greater than 2 but less than 8) and C = { multiples of 2 less than 9).
a) List the elements of U, A, B and C.
b) 0< x-2 <2
4
- 1/2
f) Find (AU B) n (AUC)
g) What can you say about AU (BNC) = (AU B) n (AU C)?
2 ≥1
d) Find (An B) U (ANC)
What can you say about An (BU C) and (ANB) U (ANC)?
e) Find AUB and A UC
--
-22-
2. Solve and graph each of the following inequalities.
a) 2x - 5<11 and 3x + 2 ≤ 20
b) x²-x-6> 0
c) 3m - 2(2m - 7) ≤2(3+m) -4
d) 3y - [7-(2-y)] ≥y +8
3. Solve each absolute value inequality and graph the solution set where
possible.
a) 3 5x-6 -722
b) 6-2x-6 > 4
4. Solve and graph 3
4
+
4
5. Solve and graph Bx + 5 = 4
6. In the problems below, what value of x each hold?
a) x-2-2x - 7
b) 3x + 5 = 2x + 6
++
9. Express the following inequalities in the form |x-a < b.
a) -5<x<7
b) 3<x<9
c) -3<x< 11
10.Solve the following inequalities and sketch the solution on the real number
line.
a) -8 ≤ (3x + 5) < 13](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F971dcec7-333f-410d-8a1c-34c358c10131%2Fab1d5e18-bd57-42c3-8087-da3b29e04893%2F3vd0ihg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Step 2:
Step 3:
5.
(2x + 1)(x-4) ≥ 0
(2x +1)(x-4)= 0
2x + 1 = 0,
x-2
2
2x = 1,
x = - ¹1/₂
x²-1
x²-9
20
x-4=0
x=4
Factorize
Find the zeros of the equation
The intervals (-∞, - ¹1/2] U [4, ∞) satisfy the inequality 2x² - 7x2 4.
Solve and graph the following inequalities. (Student problems)
1. x25x26
2. x24x5<0
3. x³-4x ≥ 0
4. 1
3
X
++
-21-
-
c) 7-2x = 5-x
d) 2x + 7 6-3x = 8
+
b) Represent U, A, B, and C on a Venn diagram.
c) Find BUC and A n (BUC)
x+1 x +3
- 1¹/2
+
Written Exercise 1
1. Given that U is a universal set that contains all whole numbers less than 10
and A and B are subset of U. Suppose A (all factors of 18), B-{natural
numbers greater than 2 but less than 8) and C = { multiples of 2 less than 9).
a) List the elements of U, A, B and C.
b) 0< x-2 <2
4
- 1/2
f) Find (AU B) n (AUC)
g) What can you say about AU (BNC) = (AU B) n (AU C)?
2 ≥1
d) Find (An B) U (ANC)
What can you say about An (BU C) and (ANB) U (ANC)?
e) Find AUB and A UC
--
-22-
2. Solve and graph each of the following inequalities.
a) 2x - 5<11 and 3x + 2 ≤ 20
b) x²-x-6> 0
c) 3m - 2(2m - 7) ≤2(3+m) -4
d) 3y - [7-(2-y)] ≥y +8
3. Solve each absolute value inequality and graph the solution set where
possible.
a) 3 5x-6 -722
b) 6-2x-6 > 4
4. Solve and graph 3
4
+
4
5. Solve and graph Bx + 5 = 4
6. In the problems below, what value of x each hold?
a) x-2-2x - 7
b) 3x + 5 = 2x + 6
++
9. Express the following inequalities in the form |x-a < b.
a) -5<x<7
b) 3<x<9
c) -3<x< 11
10.Solve the following inequalities and sketch the solution on the real number
line.
a) -8 ≤ (3x + 5) < 13
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