Question

multiple choice
circle the correct answer.

1. solve for x:

2(3x - 5) = 4x + 6
a. x = 4 b. x = 5 c. x = 6 d. x = 8

1. which expression is equivalent to:

(x - 3)² - (x + 1)(x - 1)
a. -6x + 10 b. -6x + 8 c. -4x + 10 d. -4x + 8

1. if f(x) = 2x² - 3x + 1, find f(-2).

a. 3 b. 9 c. 15 d. 19

Explanation:

Step1: Expand left side

$2(3x - 5) = 6x - 10$

Step2: Rearrange equation

$6x - 10 = 4x + 6$
$6x - 4x = 6 + 10$

Step3: Simplify to solve x

$2x = 16$
$x = \frac{16}{2} = 8$

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Step1: Expand squared term

$(x - 3)^2 = x^2 - 6x + 9$

Step2: Expand difference of squares

$(x + 1)(x - 1) = x^2 - 1$

Step3: Subtract and simplify

$(x^2 - 6x + 9) - (x^2 - 1) = x^2 -6x +9 -x^2 +1 = -6x +10$

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Step1: Substitute $x=-2$

$f(-2) = 2(-2)^2 - 3(-2) + 1$

Step2: Calculate each term

$2(-2)^2 = 2\times4=8$, $-3(-2)=6$

Step3: Sum terms

$8 + 6 + 1 = 15$

Answer:

1. D. x = 8
2. A. -6x + 10
3. C. 15