Multi-Step Equations with Decimals Worksheets - Free Printable

Let’s solve each of the 8 multi-step equations involving decimals step by step.

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1) 8(6.9c - 0.7 + 1.1c) = 7.2

Step 1: Combine like terms inside the parentheses.
→ 6.9c + 1.1c = 8c
So:
8(8c - 0.7) = 7.2

Step 2: Distribute the 8.
→ 8 × 8c = 64c
→ 8 × (-0.7) = -5.6
So:
64c - 5.6 = 7.2

Step 3: Add 5.6 to both sides.
→ 64c = 7.2 + 5.6 = 12.8

Step 4: Divide by 64.
→ c = 12.8 / 64 = 0.2

✔ Answer: c = 0.2

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2) 8 + 1.7r = -2r - 4 - 0.3r

Step 1: Combine like terms on the right side.
→ -2r - 0.3r = -2.3r
So:
8 + 1.7r = -2.3r - 4

Step 2: Add 2.3r to both sides.
→ 8 + 1.7r + 2.3r = -4
→ 8 + 4r = -4

Step 3: Subtract 8 from both sides.
→ 4r = -4 - 8 = -12

Step 4: Divide by 4.
→ r = -12 / 4 = -3

✔ Answer: r = -3

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3) 3(2t - 1.6 + t) = 5.1

Step 1: Combine like terms inside parentheses.
→ 2t + t = 3t
So:
3(3t - 1.6) = 5.1

Step 2: Distribute the 3.
→ 3 × 3t = 9t
→ 3 × (-1.6) = -4.8
So:
9t - 4.8 = 5.1

Step 3: Add 4.8 to both sides.
→ 9t = 5.1 + 4.8 = 9.9

Step 4: Divide by 9.
→ t = 9.9 / 9 = 1.1

✔ Answer: t = 1.1

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4) 5 = (6k - 2.8)/(k + 1.2)

This is a rational equation. Multiply both sides by (k + 1.2) to eliminate the denominator.

Step 1: Multiply both sides by (k + 1.2)
→ 5(k + 1.2) = 6k - 2.8

Step 2: Distribute the 5.
→ 5k + 6 = 6k - 2.8

Step 3: Subtract 5k from both sides.
→ 6 = k - 2.8

Step 4: Add 2.8 to both sides.
→ k = 6 + 2.8 = 8.8

✔ Answer: k = 8.8

*(Check: Plug back in — (6×8.8 - 2.8)/(8.8 + 1.2) = (52.8 - 2.8)/10 = 50/10 = 5 ✓)*

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5) 3(9.3 - 1.6v) = 9(-0.7v + 3.8)

Step 1: Distribute on both sides.
Left: 3 × 9.3 = 27.9; 3 × (-1.6v) = -4.8v → 27.9 - 4.8v
Right: 9 × (-0.7v) = -6.3v; 9 × 3.8 = 34.2 → -6.3v + 34.2

Equation:
27.9 - 4.8v = -6.3v + 34.2

Step 2: Add 6.3v to both sides.
→ 27.9 + 1.5v = 34.2

Step 3: Subtract 27.9 from both sides.
→ 1.5v = 34.2 - 27.9 = 6.3

Step 4: Divide by 1.5.
→ v = 6.3 / 1.5 = 4.2

✔ Answer: v = 4.2

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6) u - 8.1 = 4.3 - (u - 8)

Step 1: Distribute the negative sign on the right.
→ u - 8.1 = 4.3 - u + 8
→ u - 8.1 = 12.3 - u

Step 2: Add u to both sides.
→ 2u - 8.1 = 12.3

Step 3: Add 8.1 to both sides.
→ 2u = 12.3 + 8.1 = 20.4

Step 4: Divide by 2.
→ u = 20.4 / 2 = 10.2

✔ Answer: u = 10.2

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7) 9.6 - (8.2 + 0.5n) = 3.5n - 2.6

Step 1: Distribute the negative sign.
→ 9.6 - 8.2 - 0.5n = 3.5n - 2.6
→ 1.4 - 0.5n = 3.5n - 2.6

Step 2: Add 0.5n to both sides.
→ 1.4 = 4n - 2.6

Step 3: Add 2.6 to both sides.
→ 4.0 = 4n

Step 4: Divide by 4.
→ n = 4.0 / 4 = 1

✔ Answer: n = 1

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8) (7.5(2a - 2.2))/3 = 10

Step 1: Multiply both sides by 3 to eliminate denominator.
→ 7.5(2a - 2.2) = 30

Step 2: Divide both sides by 7.5.
→ 2a - 2.2 = 30 / 7.5 = 4

Step 3: Add 2.2 to both sides.
→ 2a = 4 + 2.2 = 6.2

Step 4: Divide by 2.
→ a = 6.2 / 2 = 3.1

✔ Answer: a = 3.1

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## ✔ Final Answers:

1) c = 0.2
2) r = -3
3) t = 1.1
4) k = 8.8
5) v = 4.2
6) u = 10.2
7) n = 1
8) a = 3.1

Let me know if you’d like to see any step explained further!