Multi Step Equations Worksheets - Math Monks - Free Printable

Let’s solve each equation one by one, step by step. I’ll show you how to isolate the variable (like n, p, x, etc.) on one side of the equation.

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1) -2(3n + 9) = 30

First, distribute the -2:
→ -6n - 18 = 30

Add 18 to both sides:
→ -6n = 48

Divide by -6:
→ n = -8

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2) 9p + 9 - 5 = -12 + 6p

Simplify left side: 9p + 4 = -12 + 6p

Subtract 6p from both sides:
→ 3p + 4 = -12

Subtract 4:
→ 3p = -16

Divide by 3:
→ p = -16/3 → But wait — let me check if this is an integer problem? The title says “Integers”, so maybe I made a mistake?

Wait — let’s recheck:

Original: 9p + 9 - 5 = -12 + 6p
→ 9p + 4 = -12 + 6p
Subtract 6p: 3p + 4 = -12
Subtract 4: 3p = -16
Yes, p = -16/3 — but that’s not an integer. Hmm. Maybe it’s okay? Or did I misread?

Actually, looking back at the worksheet title: “Multi-Step Equations: Integers” — probably means we’re working with integers in the equations, not necessarily that answers are integers. So we’ll keep it as fraction unless told otherwise.

But let me double-check arithmetic:

Left: 9p + 9 - 5 = 9p + 4 ✔️
Right: -12 + 6p ✔️
Move terms: 9p - 6p = -12 - 4 → 3p = -16 → p = -16/3 ✔️

So answer is p = -16/3

But maybe they want mixed number? No, better leave as improper fraction.

Wait — perhaps I should write all answers as simplified fractions or integers. Let’s proceed and see others.

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3) 18n - 6(-4n - 6) = 18 + 8n

Distribute the -6:
→ 18n + 24n + 36 = 18 + 8n
(Because -6 * -4n = +24n; -6 * -6 = +36)

Combine like terms on left:
→ 42n + 36 = 18 + 8n

Subtract 8n:
→ 34n + 36 = 18

Subtract 36:
→ 34n = -18

Divide by 34:
→ n = -18/34 = -9/17

Hmm again not integer. Okay, moving on.

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4) 1 + 8p - 4p + 5 = 2(p - 3) - 2(p - 2)

Simplify left: 1 + 5 = 6; 8p - 4p = 4p → 4p + 6

Right side: distribute 2 and -2:
→ 2p - 6 - 2p + 4 → (2p - 2p) + (-6 + 4) = 0p - 2 = -2

So equation becomes:
→ 4p + 6 = -2

Subtract 6:
→ 4p = -8

Divide by 4:
→ p = -2

Nice! Integer.

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5) -8x + 16 = -16x + 32

Add 16x to both sides:
→ 8x + 16 = 32

Subtract 16:
→ 8x = 16

Divide by 8:
→ x = 2

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6) 16(5 - 4v) = -5 - v

Distribute 16:
→ 80 - 64v = -5 - v

Add 64v to both sides:
→ 80 = -5 + 63v

Add 5:
→ 85 = 63v

Divide by 63:
→ v = 85/63

Can simplify? 85 and 63 share no common factors (85=5×17, 63=7×9), so leave as is.

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7) -12 = 2(2x + 4) - (7 - 3x)

First, distribute:
→ -12 = 4x + 8 - 7 + 3x [because minus (7 - 3x) = -7 + 3x]

Combine right side:
→ -12 = (4x + 3x) + (8 - 7) = 7x + 1

Subtract 1:
→ -13 = 7x

Divide by 7:
→ x = -13/7

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8) -7r - 3r = -13 - 7 - r

Left: -10r
Right: -20 - r

So:
→ -10r = -20 - r

Add r to both sides:
→ -9r = -20

Divide by -9:
→ r = 20/9

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9) 16 + 32q + 4 = -32q + 40

Left: 20 + 32q
Right: -32q + 40

Add 32q to both sides:
→ 20 + 64q = 40

Subtract 20:
→ 64q = 20

Divide by 64:
→ q = 20/64 = 5/16

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10) -6x + 14 = 1 - 8x

Add 8x to both sides:
→ 2x + 14 = 1

Subtract 14:
→ 2x = -13

Divide by 2:
→ x = -13/2

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Now, let me verify a couple to make sure I didn’t make calculation errors.

Check #1: -2(3*(-8)+9) = -2(-24+9)= -2(-15)=30 ✔️

Check #4: Left: 1 + 8*(-2) -4*(-2) +5 = 1 -16 +8 +5 = (1+8+5)-16=14-16=-2
Right: 2(-2-3) -2(-2-2)=2(-5)-2(-4)= -10 +8 = -2 ✔️

Check #5: -8*2 +16 = -16+16=0; -16*2 +32= -32+32=0 ✔️

Okay, seems correct.

Final Answers:

1) n = -8
2) p = -16/3
3) n = -9/17
4) p = -2
5) x = 2
6) v = 85/63
7) x = -13/7
8) r = 20/9
9) q = 5/16
10) x = -13/2

Note: Some answers are fractions — that’s fine since the problem didn’t specify only integer solutions, just that we’re solving multi-step equations involving integers.

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Final Answer:
1) n = -8
2) p = -16/3
3) n = -9/17
4) p = -2
5) x = 2
6) v = 85/63
7) x = -13/7
8) r = 20/9
9) q = 5/16
10) x = -13/2