Let’s solve each equation step by step. We’ll isolate the variable (like x, y, or w) on one side of the equals sign.
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1. 5x – 7 = 23
Step 1: Add 7 to both sides to cancel out the -7.
→ 5x – 7 + 7 = 23 + 7
→ 5x = 30
Step 2: Divide both sides by 5 to get x alone.
→ 5x ÷ 5 = 30 ÷ 5
→ x = 6
✔ Check: 5(6) – 7 = 30 – 7 = 23 → Correct!
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2. 4x – 15 = 1
Step 1: Add 15 to both sides.
→ 4x – 15 + 15 = 1 + 15
→ 4x = 16
Step 2: Divide both sides by 4.
→ 4x ÷ 4 = 16 ÷ 4
→ x = 4
✔ Check: 4(4) – 15 = 16 – 15 = 1 → Correct!
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3. 2y + 3 = -11
Step 1: Subtract 3 from both sides.
→ 2y + 3 – 3 = -11 – 3
→ 2y = -14
Step 2: Divide both sides by 2.
→ 2y ÷ 2 = -14 ÷ 2
→ y = -7
✔ Check: 2(-7) + 3 = -14 + 3 = -11 → Correct!
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4. 2y + 7 = -7
Step 1: Subtract 7 from both sides.
→ 2y + 7 – 7 = -7 – 7
→ 2y = -14
Step 2: Divide both sides by 2.
→ 2y ÷ 2 = -14 ÷ 2
→ y = -7
✔ Check: 2(-7) + 7 = -14 + 7 = -7 → Correct!
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5. x/2 + 7 = 1
Step 1: Subtract 7 from both sides.
→ x/2 + 7 – 7 = 1 – 7
→ x/2 = -6
Step 2: Multiply both sides by 2 to cancel the denominator.
→ 2 × (x/2) = -6 × 2
→ x = -12
✔ Check: (-12)/2 + 7 = -6 + 7 = 1 → Correct!
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6. 3w + 3 = 3
Step 1: Subtract 3 from both sides.
→ 3w + 3 – 3 = 3 – 3
→ 3w = 0
Step 2: Divide both sides by 3.
→ 3w ÷ 3 = 0 ÷ 3
→ w = 0
✔ Check: 3(0) + 3 = 0 + 3 = 3 → Correct!
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Final Answer:
1. x = 6
2. x = 4
3. y = -7
4. y = -7
5. x = -12
6. w = 0
Parent Tip: Review the logic above to help your child master the concept of solving equations practice worksheet.
