Question

1. for what value of x is the equation 2(x + 7) = 3(x + 11) true? a. -19 b. -4 c. 18 d. 19 2. what is the value of x that satisfies the equation 3(x - 2) = 6x + 5? f. $-\frac{11}{3}$ g. $-\frac{7}{3}$ h. -1 j. 1 3. if 5(x - 3) + 11 = 6, what is the value of x? a. $-\frac{2}{5}$ b. -4 c. 2 d. 4

Explanation:

Problem 1

Step1: Expand both sides

$2x + 14 = 3x + 33$

Step2: Isolate x terms

$2x - 3x = 33 - 14$

Step3: Simplify to solve x

$-x = 19 \implies x = -19$

Problem 2

Step1: Expand left side

$3x - 6 = 6x + 5$

Step2: Isolate x terms

$3x - 6x = 5 + 6$

Step3: Simplify to solve x

$-3x = 11 \implies x = -\frac{11}{3}$

Problem 3

Step1: Expand left side

$5x - 15 + 11 = 6$

Step2: Simplify constants

$5x - 4 = 6$

Step3: Isolate x term

$5x = 6 + 4$

Step4: Simplify to solve x

$5x = 10 \implies x = 2$

Answer:

1. A. -19
2. F. $-\frac{11}{3}$
3. C. 2