Let’s solve each equation step by step. We’re solving for
x in each case.
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1.) 5x - 1 = -31
Add 1 to both sides:
→ 5x = -30
Divide by 5:
→ x = -6
✔ Check: 5*(-6) - 1 = -30 -1 = -31 → Correct.
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2.) 2 + 6x = 32
Subtract 2 from both sides:
→ 6x = 30
Divide by 6:
→ x = 5
✔ Check: 2 + 6*5 = 2 + 30 = 32 → Correct.
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3.) 8x + 1 = 7
Subtract 1:
→ 8x = 6
Divide by 8:
→ x = 6/8 = 3/4 or 0.75
✔ Check: 8*(0.75) + 1 = 6 + 1 = 7 → Correct.
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4.) 5 - 3x = 8
Subtract 5:
→ -3x = 3
Divide by -3:
→ x = -1
✔ Check: 5 - 3*(-1) = 5 + 3 = 8 → Correct.
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5.) 9x + 8 = 62
Subtract 8:
→ 9x = 54
Divide by 9:
→ x = 6
✔ Check: 9*6 + 8 = 54 + 8 = 62 → Correct.
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6.) 2x + 5 = 5
Subtract 5:
→ 2x = 0
Divide by 2:
→ x = 0
✔ Check: 2*0 + 5 = 0 + 5 = 5 → Correct.
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7.) -8x + 7 = 71
Subtract 7:
→ -8x = 64
Divide by -8:
→ x = -8
✔ Check: -8*(-8) + 7 = 64 + 7 = 71 → Correct.
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8.) 3 - 2x = 5
Subtract 3:
→ -2x = 2
Divide by -2:
→ x = -1
✔ Check: 3 - 2*(-1) = 3 + 2 = 5 → Correct.
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9.) 7 + 4x = 47
Subtract 7:
→ 4x = 40
Divide by 4:
→ x = 10
✔ Check: 7 + 4*10 = 7 + 40 = 47 → Correct.
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10.) 7x - 2 = 47
Add 2:
→ 7x = 49
Divide by 7:
→ x = 7
✔ Check: 7*7 - 2 = 49 - 2 = 47 → Correct.
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11.) -7x + 3 = -53
Subtract 3:
→ -7x = -56
Divide by -7:
→ x = 8
✔ Check: -7*8 + 3 = -56 + 3 = -53 → Correct.
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12.) 6 - 6x = 18
Subtract 6:
→ -6x = 12
Divide by -6:
→ x = -2
✔ Check: 6 - 6*(-2) = 6 + 12 = 18 → Correct.
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Final Answer:
1.) x = -6
2.) x = 5
3.) x = 3/4 (or 0.75)
4.) x = -1
5.) x = 6
6.) x = 0
7.) x = -8
8.) x = -1
9.) x = 10
10.) x = 7
11.) x = 8
12.) x = -2
Parent Tip: Review the logic above to help your child master the concept of solving two step equations worksheet 7th grade.
