I will solve all the linear equations in the worksheet step by step, checking my work as I go.
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Section A
1) 7x + 9 = 23
→ Subtract 9 from both sides: 7x = 14
→ Divide by 7: x = 2
✔
2) 5x + 7 = 42
→ Subtract 7: 5x = 35
→ Divide by 5: x = 7
✔
3) 4x + 3 = 51
→ Subtract 3: 4x = 48
→ Divide by 4: x = 12
✔
4) 9x + 5 = 41
→ Subtract 5: 9x = 36
→ Divide by 9: x = 4
✔
5) 4x + 2 = 34
→ Subtract 2: 4x = 32
→ Divide by 4: x = 8
✔
6) 11x + 3 = 36
→ Subtract 3: 11x = 33
→ Divide by 11: x = 3
✔
7) 10x + 2 = 72
→ Subtract 2: 10x = 70
→ Divide by 10: x = 7
✔
8) 7x + 3 = 52
→ Subtract 3: 7x = 49
→ Divide by 7: x = 7
✔
9) 6x + 5 = 17
→ Subtract 5: 6x = 12
→ Divide by 6: x = 2
✔
10) 4x + 7 = 9
→ Subtract 7: 4x = 2
→ Divide by 4: x = 0.5
✔
11) 8x + 11 = 15
→ Subtract 11: 8x = 4
→ Divide by 8: x = 0.5
✔
12) 4x + 17 = 18
→ Subtract 17: 4x = 1
→ Divide by 4: x = 0.25
✔
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Section B
1) 1 + 6x = 19
→ Subtract 1: 6x = 18
→ Divide by 6: x = 3
✔
2) 9 + 7x = 30
→ Subtract 9: 7x = 21
→ Divide by 7: x = 3
✔
3) 3 + 2x = 17
→ Subtract 3: 2x = 14
→ Divide by 2: x = 7
✔
4) 11 + 5x = 71
→ Subtract 11: 5x = 60
→ Divide by 5: x = 12
✔
5) 5 + 3x = 32
→ Subtract 5: 3x = 27
→ Divide by 3: x = 9
✔
6) 4 + 5x = 44
→ Subtract 4: 5x = 40
→ Divide by 5: x = 8
✔
7) 23 = x + 8
→ Subtract 8: x = 15
✔
8) 28 = 3x + 1
→ Subtract 1: 27 = 3x
→ Divide by 3: x = 9
✔
9) 53 = 8x + 5
→ Subtract 5: 48 = 8x
→ Divide by 8: x = 6
✔
10) 13 = 11 + 4x
→ Subtract 11: 2 = 4x
→ Divide by 4: x = 0.5
✔
11) 7 = 8x + 3
→ Subtract 3: 4 = 8x
→ Divide by 8: x = 0.5
✔
12) 12 = 7 + 15x
→ Subtract 7: 5 = 15x
→ Divide by 15: x = 1/3 ≈ 0.333...
✔
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Section C
1) 4x - 1 = 31
→ Add 1: 4x = 32
→ Divide by 4: x = 8
✔
2) 3x - 4 = 29
→ Add 4: 3x = 33
→ Divide by 3: x = 11
✔
3) 6x - 5 = 31
→ Add 5: 6x = 36
→ Divide by 6: x = 6
✔
4) 8x - 2 = 46
→ Add 2: 8x = 48
→ Divide by 8: x = 6
✔
5) 2x - 7 = 21
→ Add 7: 2x = 28
→ Divide by 2: x = 14
✔
6) 7x - 3 = 18
→ Add 3: 7x = 21
→ Divide by 7: x = 3
✔
7) 9x - 4 = 32
→ Add 4: 9x = 36
→ Divide by 9: x = 4
✔
8) 5x - 1 = 64
→ Add 1: 5x = 65
→ Divide by 5: x = 13
✔
9) 12x - 9 = 39
→ Add 9: 12x = 48
→ Divide by 12: x = 4
✔
10) 2x - 1 = 2
→ Add 1: 2x = 3
→ Divide by 2: x = 1.5
✔
11) 4x - 8 = 10
→ Add 8: 4x = 18
→ Divide by 4: x = 4.5
✔
12) 15x - 2 = 3
→ Add 2: 15x = 5
→ Divide by 15: x = 1/3 ≈ 0.333...
✔
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Final Answer:
Section A:
1) x=2, 2) x=7, 3) x=12, 4) x=4, 5) x=8, 6) x=3, 7) x=7, 8) x=7, 9) x=2, 10) x=0.5, 11) x=0.5, 12) x=0.25
Section B:
1) x=3, 2) x=3, 3) x=7, 4) x=12, 5) x=9, 6) x=8, 7) x=15, 8) x=9, 9) x=6, 10) x=0.5, 11) x=0.5, 12) x=1/3
Section C:
1) x=8, 2) x=11, 3) x=6, 4) x=6, 5) x=14, 6) x=3, 7) x=4, 8) x=13, 9) x=4, 10) x=1.5, 11) x=4.5, 12) x=1/3
Parent Tip: Review the logic above to help your child master the concept of simple algebra worksheet for grade 7.
