Let’s solve each equation step by step. We’ll isolate the variable on one side of the equation using inverse operations — that means undoing what’s being done to the variable.
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1) -5.6p + 12.9 = -1.3p
Step 1: Get all terms with “p” on one side. Add 5.6p to both sides:
→ 12.9 = -1.3p + 5.6p
→ 12.9 = 4.3p
Step 2: Divide both sides by 4.3:
→ p = 12.9 ÷ 4.3
→ p = 3
✔ Check: Plug back in:
Left: -5.6(3) + 12.9 = -16.8 + 12.9 = -3.9
Right: -1.3(3) = -3.9 → Correct!
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2) -7.7 - n = 1
Step 1: Add 7.7 to both sides:
→ -n = 1 + 7.7
→ -n = 8.7
Step 2: Multiply both sides by -1:
→ n = -8.7
✔ Check: -7.7 - (-8.7) = -7.7 + 8.7 = 1 → Correct!
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3) 9.1 = 2y + 3.5
Step 1: Subtract 3.5 from both sides:
→ 9.1 - 3.5 = 2y
→ 5.6 = 2y
Step 2: Divide by 2:
→ y = 5.6 ÷ 2
→ y = 2.8
✔ Check: 2(2.8) + 3.5 = 5.6 + 3.5 = 9.1 → Correct!
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4) -6.5 = d / 0.2 - 12
Step 1: Add 12 to both sides:
→ -6.5 + 12 = d / 0.2
→ 5.5 = d / 0.2
Step 2: Multiply both sides by 0.2:
→ d = 5.5 × 0.2
→ d = 1.1
✔ Check: 1.1 / 0.2 = 5.5; 5.5 - 12 = -6.5 → Correct!
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5) (v - 10.9)/5 = -8.4
Step 1: Multiply both sides by 5:
→ v - 10.9 = -8.4 × 5
→ v - 10.9 = -42
Step 2: Add 10.9 to both sides:
→ v = -42 + 10.9
→ v = -31.1
✔ Check: (-31.1 - 10.9)/5 = (-42)/5 = -8.4 → Correct!
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6) -c - 2.1 = -14.7
Step 1: Add 2.1 to both sides:
→ -c = -14.7 + 2.1
→ -c = -12.6
Step 2: Multiply both sides by -1:
→ c = 12.6
✔ Check: -12.6 - 2.1 = -14.7 → Correct!
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7) 7.3r - 15 = 6.3r
Step 1: Subtract 6.3r from both sides:
→ 7.3r - 6.3r - 15 = 0
→ 1.0r - 15 = 0
→ r - 15 = 0
Step 2: Add 15 to both sides:
→ r = 15
✔ Check: 7.3(15) - 15 = 109.5 - 15 = 94.5; 6.3(15) = 94.5 → Correct!
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8) 3.6 = 1.5(8.8 + x)
Step 1: Divide both sides by 1.5:
→ 3.6 ÷ 1.5 = 8.8 + x
→ 2.4 = 8.8 + x
Step 2: Subtract 8.8 from both sides:
→ x = 2.4 - 8.8
→ x = -6.4
✔ Check: 1.5(8.8 + (-6.4)) = 1.5(2.4) = 3.6 → Correct!
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Final Answer:
1) p = 3
2) n = -8.7
3) y = 2.8
4) d = 1.1
5) v = -31.1
6) c = 12.6
7) r = 15
8) x = -6.4
Parent Tip: Review the logic above to help your child master the concept of solving equations with decimals worksheet.
