Question

two-step equations

1. $-12x - 6 = 18$
2. $\frac{x}{5} - 17 = -24$
3. $108 = -8x - 20$
4. $-1 + 4x = 31$
5. $\frac{x}{15} + 12 = 13$
6. $\frac{x + 6}{13} = 2$
7. $-20 - x = -27$
8. $-7 = \frac{x}{3} + 2$
9. $6(x + 15) = -102$

solution

1. $x =$

2)
3)
4)
5)
6)
7)
8)
9)

Explanation:

Step1: Isolate the term with $x$

Add 6 to both sides:
$-12x - 6 + 6 = 18 + 6$
$-12x = 24$

Step2: Solve for $x$

Divide by $-12$:
$x = \frac{24}{-12}$
$x = -2$

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Step1: Isolate the term with $x$

Add 17 to both sides:
$\frac{x}{5} - 17 + 17 = -24 + 17$
$\frac{x}{5} = -7$

Step2: Solve for $x$

Multiply by 5:
$x = -7 \times 5$
$x = -35$

---

Step1: Isolate the term with $x$

Add 20 to both sides:
$108 + 20 = -8x - 20 + 20$
$128 = -8x$

Step2: Solve for $x$

Divide by $-8$:
$x = \frac{128}{-8}$
$x = -16$

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Step1: Isolate the term with $x$

Add 1 to both sides:
$-1 + 1 + 4x = 31 + 1$
$4x = 32$

Step2: Solve for $x$

Divide by 4:
$x = \frac{32}{4}$
$x = 8$

---

Step1: Isolate the term with $x$

Subtract 12 from both sides:
$\frac{x}{15} + 12 - 12 = 13 - 12$
$\frac{x}{15} = 1$

Step2: Solve for $x$

Multiply by 15:
$x = 1 \times 15$
$x = 15$

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Step1: Eliminate the denominator

Multiply by 13:
$\frac{x+6}{13} \times 13 = 2 \times 13$
$x + 6 = 26$

Step2: Solve for $x$

Subtract 6:
$x = 26 - 6$
$x = 20$

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Step1: Isolate the term with $x$

Add 20 to both sides:
$-20 + 20 - x = -27 + 20$
$-x = -7$

Step2: Solve for $x$

Multiply by $-1$:
$x = 7$

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Step1: Isolate the term with $x$

Subtract 2 from both sides:
$-7 - 2 = \frac{x}{3} + 2 - 2$
$-9 = \frac{x}{3}$

Step2: Solve for $x$

Multiply by 3:
$x = -9 \times 3$
$x = -27$

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Step1: Eliminate the coefficient

Divide by 6:
$\frac{6(x+15)}{6} = \frac{-102}{6}$
$x + 15 = -17$

Step2: Solve for $x$

Subtract 15:
$x = -17 - 15$
$x = -32$

Answer:

1. $x = -2$
2. $x = -35$
3. $x = -16$
4. $x = 8$
5. $x = 15$
6. $x = 20$
7. $x = 7$
8. $x = -27$
9. $x = -32$