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 of eq1

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

Step2: Isolate x terms (eq1)

$6x - 4x = 6 + 10$

Step3: Simplify to solve x (eq1)

$2x = 16 \implies x = 8$

Step4: Expand both terms (eq2)

$(x-3)^2 = x^2 -6x +9$; $(x+1)(x-1)=x^2 -1$

Step5: Subtract and simplify (eq2)

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

Step6: Substitute x=-2 (eq3)

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

Step7: Calculate f(-2)

$2(4) +6 +1 = 8+6+1=15$

Answer:

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