Question

directions: solve and check. show all

1. $-4(x + 2) = -16$

solve
$-4(x+2)=-16$
$-4(x+2)=-16$
$-4(x)-4(2)=-16$
$-4x - 8 = -16$
$+8 = +8$
$0 = -8$
$x = 2$
check
$-4(x+2)=-16$
$-4(2+2)=-16$
$-4(4)$
$-16$ ok

1. $15 = 3(z - 2)$

solve
$15 = 3(z - 2)$
$15 = 3*1(z) + 1(z)$
$15 = 3 + x + 2$
$15 = x + 5$
$-5 -5$
$10 = x$
check
(blank)

1. $17 - 2(b + 12) = 7$

(blank)

1. $2 + 3(2d + 3) = -7$

(blank)

Explanation:

Problem 3:

Step1: Divide both sides by 3

$\frac{15}{3} = \frac{3(z-2)}{3}$
$5 = z - 2$

Step2: Add 2 to both sides

$5 + 2 = z - 2 + 2$
$z = 7$

Step3: Check solution

Substitute $z=7$ into $15=3(z-2)$:
$15 = 3(7-2)$
$15 = 3(5)$
$15 = 15$

Problem 5:

Step1: Distribute the -2

$17 - 2b - 24 = 7$

Step2: Combine like terms

$-2b -7 = 7$

Step3: Add 7 to both sides

$-2b -7 +7 = 7 +7$
$-2b = 14$

Step4: Divide by -2

$\frac{-2b}{-2} = \frac{14}{-2}$
$b = -7$

Step5: Check solution

Substitute $b=-7$ into $17-2(b+12)=7$:
$17 - 2(-7+12) = 7$
$17 - 2(5) = 7$
$17 -10 =7$
$7=7$

Problem 7:

Step1: Distribute the 3

$2 + 6d +9 = -7$

Step2: Combine like terms

$6d +11 = -7$

Step3: Subtract 11 from both sides

$6d +11 -11 = -7 -11$
$6d = -18$

Step4: Divide by 6

$\frac{6d}{6} = \frac{-18}{6}$
$d = -3$

Step5: Check solution

Substitute $d=-3$ into $2+3(2d+3)=-7$:
$2 + 3(2(-3)+3) = -7$
$2 + 3(-6+3) = -7$
$2 + 3(-3) = -7$
$2 -9 = -7$
$-7=-7$

Answer:

Problem 3: $z=7$
Problem 5: $b=-7$
Problem 7: $d=-3$