Solving Equations using Equality Properties of Addition ... - Free Printable

Let’s solve each problem one by one. We’ll isolate the variable x in each equation to find its value.

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Problem 3: 5x – 8 = 12

Step 1: Add 8 to both sides
→ 5x = 12 + 8 → 5x = 20

Step 2: Divide both sides by 5
→ x = 20 ÷ 5 → x = 4

✔ Answer: b. 4

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Problem 4: 3x + 9 = 18

Step 1: Subtract 9 from both sides
→ 3x = 18 – 9 → 3x = 9

Step 2: Divide both sides by 3
→ x = 9 ÷ 3 → x = 3

✔ Answer: d. 3

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Problem 5: x/6 + 1 = 4

Step 1: Subtract 1 from both sides
→ x/6 = 4 – 1 → x/6 = 3

Step 2: Multiply both sides by 6
→ x = 3 × 6 → x = 18

✔ Answer: a. 18

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Problem 6: x/2 – 3 = 7

Step 1: Add 3 to both sides
→ x/2 = 7 + 3 → x/2 = 10

Step 2: Multiply both sides by 2
→ x = 10 × 2 → x = 20

✔ Answer: d. 20

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Problem 7: x/5 + 1 = –2

Step 1: Subtract 1 from both sides
→ x/5 = –2 – 1 → x/5 = –3

Step 2: Multiply both sides by 5
→ x = –3 × 5 → x = –15

✔ Answer: b. –15

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Problem 8: x/4 – 3 = –5

Step 1: Add 3 to both sides
→ x/4 = –5 + 3 → x/4 = –2

Step 2: Multiply both sides by 4
→ x = –2 × 4 → x = –8

✔ Answer: c. –8

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Problem 9: x/6 + 1 = 10

Step 1: Subtract 1 from both sides
→ x/6 = 10 – 1 → x/6 = 9

Step 2: Multiply both sides by 6
→ x = 9 × 6 → x = 54

✔ Answer: a. 54

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Problem 10: x/(–3) – 4 = 6

Note: This is the same as –x/3 – 4 = 6, but we can treat it as x divided by –3.

Step 1: Add 4 to both sides
→ x/(–3) = 6 + 4 → x/(–3) = 10

Step 2: Multiply both sides by –3
→ x = 10 × (–3) → x = –30

✔ Answer: d. –30

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Final Answer:
3. b
4. d
5. a
6. d
7. b
8. c
9. a
10. d