Multi Step Equations Worksheets - Math Monks - Free Printable

Let's solve each of the multi-step equations step by step.

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1. $\frac{3}{4}x - 7 = 8$

Step 1: Add 7 to both sides
$$
\frac{3}{4}x = 8 + 7 = 15
$$

Step 2: Multiply both sides by $\frac{4}{3}$ (the reciprocal of $\frac{3}{4}$)
$$
x = 15 \cdot \frac{4}{3} = 20
$$

✔ Answer: $x = 20$

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2. $-6 = \frac{c}{-4} + 12$

Step 1: Subtract 12 from both sides
$$
-6 - 12 = \frac{c}{-4} \Rightarrow -18 = \frac{c}{-4}
$$

Step 2: Multiply both sides by $-4$
$$
c = (-18)(-4) = 72
$$

✔ Answer: $c = 72$

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3. $6 - \frac{3}{4}k = -4$

Step 1: Subtract 6 from both sides
$$
-\frac{3}{4}k = -4 - 6 = -10
$$

Step 2: Multiply both sides by $-\frac{4}{3}$
$$
k = (-10) \cdot \left(-\frac{4}{3}\right) = \frac{40}{3}
$$

✔ Answer: $k = \frac{40}{3}$ or $13\frac{1}{3}$

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4. $\frac{v + 8}{-2} = 5$

Step 1: Multiply both sides by $-2$
$$
v + 8 = 5 \cdot (-2) = -10
$$

Step 2: Subtract 8 from both sides
$$
v = -10 - 8 = -18
$$

✔ Answer: $v = -18$

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5. $3.2e + 2.6 = -23$

Step 1: Subtract 2.6 from both sides
$$
3.2e = -23 - 2.6 = -25.6
$$

Step 2: Divide both sides by 3.2
$$
e = \frac{-25.6}{3.2} = -8
$$

✔ Answer: $e = -8$

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6. $18 = 5x + 3 + 10x$

Step 1: Combine like terms on the right
$$
18 = 15x + 3
$$

Step 2: Subtract 3 from both sides
$$
15 = 15x
$$

Step 3: Divide by 15
$$
x = 1
$$

✔ Answer: $x = 1$

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7. $-7 - 2x = 7(x + 8)$

Step 1: Expand the right side
$$
-7 - 2x = 7x + 56
$$

Step 2: Move all $x$-terms to one side and constants to the other
Add $2x$ to both sides:
$$
-7 = 9x + 56
$$

Subtract 56 from both sides:
$$
-63 = 9x
$$

Step 3: Divide by 9
$$
x = -7
$$

✔ Answer: $x = -7$

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8. $9x - 4(-x + 7) = -16 + 9x$

Step 1: Expand the left side
$$
9x + 4x - 28 = -16 + 9x
\Rightarrow 13x - 28 = -16 + 9x
$$

Step 2: Subtract $9x$ from both sides
$$
4x - 28 = -16
$$

Step 3: Add 28 to both sides
$$
4x = 12
$$

Step 4: Divide by 4
$$
x = 3
$$

✔ Answer: $x = 3$

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9. $-8(3r - 2) = -8r + 40$

Step 1: Expand the left side
$$
-24r + 16 = -8r + 40
$$

Step 2: Add $24r$ to both sides
$$
16 = 16r + 40
$$

Step 3: Subtract 40 from both sides
$$
-24 = 16r
$$

Step 4: Divide by 16
$$
r = -\frac{24}{16} = -\frac{3}{2}
$$

✔ Answer: $r = -\frac{3}{2}$ or $-1.5$

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10. $10(-2 - 5n) = -30 + 10n$

Step 1: Expand the left side
$$
-20 - 50n = -30 + 10n
$$

Step 2: Add $50n$ to both sides
$$
-20 = -30 + 60n
$$

Step 3: Add 30 to both sides
$$
10 = 60n
$$

Step 4: Divide by 60
$$
n = \frac{10}{60} = \frac{1}{6}
$$

✔ Answer: $n = \frac{1}{6}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $x = 20$ |
| 2 | $c = 72$ |
| 3 | $k = \frac{40}{3}$ |
| 4 | $v = -18$ |
| 5 | $e = -8$ |
| 6 | $x = 1$ |
| 7 | $x = -7$ |
| 8 | $x = 3$ |
| 9 | $r = -\frac{3}{2}$ |
| 10 | $n = \frac{1}{6}$ |

Let me know if you'd like these explained in a different way!