Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 5, Problem 18CT

To determine

To give the letter of the correct answer of the given function of 3x2−2x−8+1x+2=4x2−16

Expert Solution & Answer

Answer to Problem 18CT

The correct answer is -3.

Explanation of Solution

Given that: : 3x2−2x−8+1x+2=4x2−16

Write (x2−16)=(x+4)(x−4)

Take factor of x2−2x−8=(x−4)(x+2)

Rewrite the given equation

3(x−4)(x+2)+1x+2=4(x−4)(x+4)

Multiply by (x−4)(x+2)(x+4) both sides, LCM of (x+2) , (x+4) and (x-4)

(x+4)(x−4)(x+2)(3(x−4)(x+2)+1x+2)=(x+4)(x−4)(x+2)(4(x−4)(x+4))

Apply distributive property

3(x+4)+(x2−16)=4(x+2)3x+12+x2−16=4x+8x2+3x−4=4x+8x2−x−12=0

Now, Apply factor method

x2−x−12=0x2−(4−3)x−12=0x2−4x+3x−12=0x(x−4)+3(x−4)=0(x+3)(x−4)=0 \

Apply zero product property to find the x value

x+3=0x=−3Similarlyx−4=0x=4

The solution set is {−3,4}

Check: verify the point for the given equation

For

(x=−3)

39+6−8+1−3+2=49−1637−1=−47−47=−47LHS=RHS

Similarly for (x=4)

316−8−8+14+2=416−16←undefined

Not verify for x=4

Hence , the set of solution is (-3)

Chapter 5, Problem 17CT

Chapter 5, Problem 19CT

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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To give the letter of the correct answer of the given function of 3 x 2 − 2 x − 8 + 1 x + 2 = 4 x 2 − 16

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To give the letter of the correct answer of the given function of 3x2−2x−8+1x+2=4x2−16

Answer to Problem 18CT

Explanation of Solution

Chapter 5 Solutions

Additional Math Textbook Solutions