Question

1. enter the value of x that makes the given equation true: 8(5 + 2x) = -24 + 8x
2. solve and graph the inequality for z: 7 < z + 15
3. solve and graph the inequality for d: -21 ≥ 3(x + 6)

Explanation:

Step1: Solve the equation for x in question 15

First, expand the left - hand side of the equation $8(5 + 2x)=-24 + 8x$.
$8\times5+8\times2x=-24 + 8x$
$40+16x=-24 + 8x$
Subtract $8x$ from both sides:
$40+16x-8x=-24 + 8x-8x$
$40 + 8x=-24$
Subtract 40 from both sides:
$40+8x - 40=-24-40$
$8x=-64$
Divide both sides by 8:
$\frac{8x}{8}=\frac{-64}{8}$
$x=-8$

Step2: Solve the inequality for z in question 16

Given $7\lt z + 15$.
Subtract 15 from both sides:
$7-15\lt z+15 - 15$
$-8\lt z$ or $z > - 8$.
To graph, draw an open circle at - 8 on the number line and shade to the right.

Step3: Solve the inequality for x in question 17

Given $-21\geq3(x + 6)$.
First, distribute the 3 on the right - hand side:
$-21\geq3x+18$
Subtract 18 from both sides:
$-21-18\geq3x+18 - 18$
$-39\geq3x$
Divide both sides by 3:
$\frac{-39}{3}\geq\frac{3x}{3}$
$-13\geq x$ or $x\leq - 13$.
To graph, draw a closed circle at - 13 on the number line and shade to the left.

Answer:

1. $x=-8$
2. $z > - 8$, graph: open circle at - 8, shade right
3. $x\leq - 13$, graph: closed circle at - 13, shade left