Let’s solve each equation step by step. Remember, we want to find the value of the variable (y or z) in each problem. We’ll do this by undoing the operations — first subtract or add, then divide.
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1. 11 + y • 5 = 61
Step 1: Subtract 11 from both sides
→ y • 5 = 61 - 11 = 50
Step 2: Divide both sides by 5
→ y = 50 ÷ 5 =
10
✔ Check: 11 + 10•5 = 11 + 50 = 61 ✔️
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2. 12 • y - 4 = 116
Step 1: Add 4 to both sides
→ 12 • y = 116 + 4 = 120
Step 2: Divide both sides by 12
→ y = 120 ÷ 12 =
10
✔ Check: 12•10 - 4 = 120 - 4 = 116 ✔️
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3. 8 • z - 12 = 4
Step 1: Add 12 to both sides
→ 8 • z = 4 + 12 = 16
Step 2: Divide both sides by 8
→ z = 16 ÷ 8 =
2
✔ Check: 8•2 - 12 = 16 - 12 = 4 ✔️
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4. 4 + y • 1 = 10
Step 1: Subtract 4 from both sides
→ y • 1 = 10 - 4 = 6
Step 2: Since multiplying by 1 doesn’t change anything,
→ y =
6
✔ Check: 4 + 6•1 = 4 + 6 = 10 ✔️
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5. 4 • y + 7 = 23
Step 1: Subtract 7 from both sides
→ 4 • y = 23 - 7 = 16
Step 2: Divide both sides by 4
→ y = 16 ÷ 4 =
4
✔ Check: 4•4 + 7 = 16 + 7 = 23 ✔️
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6. 6 + 13 • y = 175
Step 1: Subtract 6 from both sides
→ 13 • y = 175 - 6 = 169
Step 2: Divide both sides by 13
→ y = 169 ÷ 13 =
13
✔ Check: 6 + 13•13 = 6 + 169 = 175 ✔️
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7. 2 + 15 • z = 92
Step 1: Subtract 2 from both sides
→ 15 • z = 92 - 2 = 90
Step 2: Divide both sides by 15
→ z = 90 ÷ 15 =
6
✔ Check: 2 + 15•6 = 2 + 90 = 92 ✔️
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8. 13 + z • 9 = 49
Step 1: Subtract 13 from both sides
→ z • 9 = 49 - 13 = 36
Step 2: Divide both sides by 9
→ z = 36 ÷ 9 =
4
✔ Check: 13 + 4•9 = 13 + 36 = 49 ✔️
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9. 10 + z • 15 = 100
Step 1: Subtract 10 from both sides
→ z • 15 = 100 - 10 = 90
Step 2: Divide both sides by 15
→ z = 90 ÷ 15 =
6
✔ Check: 10 + 6•15 = 10 + 90 = 100 ✔️
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10. 10 • y + 2 = 22
Step 1: Subtract 2 from both sides
→ 10 • y = 22 - 2 = 20
Step 2: Divide both sides by 10
→ y = 20 ÷ 10 =
2
✔ Check: 10•2 + 2 = 20 + 2 = 22 ✔️
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Final Answer:
1. y = 10
2. y = 10
3. z = 2
4. y = 6
5. y = 4
6. y = 13
7. z = 6
8. z = 4
9. z = 6
10. y = 2
Parent Tip: Review the logic above to help your child master the concept of two step equations worksheet key.
