This worksheet provides structured practice for students learning to isolate variables in linear equations across three difficulty levels.

Let me solve all the linear equations in this worksheet step by step.

Section A:

1) 7x + 9 = 23
7x = 23 - 9 = 14
x = 14/7 = 2

2) 5x + 7 = 42
5x = 42 - 7 = 35
x = 35/5 = 7

3) 4x + 3 = 51
4x = 51 - 3 = 48
x = 48/4 = 12

4) 9x + 5 = 41
9x = 41 - 5 = 36
x = 36/9 = 4

5) 4x + 2 = 34
4x = 34 - 2 = 32
x = 32/4 = 8

6) 11x + 3 = 36
11x = 36 - 3 = 33
x = 33/11 = 3

7) 10x + 2 = 72
10x = 72 - 2 = 70
x = 70/10 = 7

8) 7x + 3 = 52
7x = 52 - 3 = 49
x = 49/7 = 7

9) 6x + 5 = 17
6x = 17 - 5 = 12
x = 12/6 = 2

10) 4x + 7 = 9
4x = 9 - 7 = 2
x = 2/4 = 0.5 or 1/2

11) 8x + 11 = 15
8x = 15 - 11 = 4
x = 4/8 = 0.5 or 1/2

12) 4x + 17 = 18
4x = 18 - 17 = 1
x = 1/4 = 0.25

Section B:

1) 1 + 6x = 19
6x = 19 - 1 = 18
x = 18/6 = 3

2) 9 + 7x = 30
7x = 30 - 9 = 21
x = 21/7 = 3

3) 3 + 2x = 17
2x = 17 - 3 = 14
x = 14/2 = 7

4) 11 + 5x = 71
5x = 71 - 11 = 60
x = 60/5 = 12

5) 5 + 3x = 32
3x = 32 - 5 = 27
x = 27/3 = 9

6) 4 + 5x = 44
5x = 44 - 4 = 40
x = 40/5 = 8

7) 23 = x + 8
x = 23 - 8 = 15

8) 28 = 3x + 1
3x = 28 - 1 = 27
x = 27/3 = 9

9) 53 = 8x + 5
8x = 53 - 5 = 48
x = 48/8 = 6

10) 13 = 11 + 4x
4x = 13 - 11 = 2
x = 2/4 = 0.5 or 1/2

11) 7 = 8x + 3
8x = 7 - 3 = 4
x = 4/8 = 0.5 or 1/2

12) 12 = 7 + 15x
15x = 12 - 7 = 5
x = 5/15 = 1/3

Section C:

1) 4x - 1 = 31
4x = 31 + 1 = 32
x = 32/4 = 8

2) 3x - 4 = 29
3x = 29 + 4 = 33
x = 33/3 = 11

3) 6x - 5 = 31
6x = 31 + 5 = 36
x = 36/6 = 6

4) 8x - 2 = 46
8x = 46 + 2 = 48
x = 48/8 = 6

5) 2x - 7 = 21
2x = 21 + 7 = 28
x = 28/2 = 14

6) 7x - 3 = 18
7x = 18 + 3 = 21
x = 21/7 = 3

7) 9x - 4 = 32
9x = 32 + 4 = 36
x = 36/9 = 4

8) 5x - 1 = 64
5x = 64 + 1 = 65
x = 65/5 = 13

9) 12x - 9 = 39
12x = 39 + 9 = 48
x = 48/12 = 4

10) 2x - 1 = 2
2x = 2 + 1 = 3
x = 3/2 = 1.5 or 3/2

11) 4x - 8 = 10
4x = 10 + 8 = 18
x = 18/4 = 4.5 or 9/2

12) 15x - 2 = 3
15x = 3 + 2 = 5
x = 5/15 = 1/3

Let me verify some of these:

Section A:
1) 7(2) + 9 = 14 + 9 = 23 ✓
2) 5(7) + 7 = 35 + 7 = 42 ✓
3) 4(12) + 3 = 48 + 3 = 51 ✓
4) 9(4) + 5 = 36 + 5 = 41 ✓
5) 4(8) + 2 = 32 + 2 = 34 ✓
6) 11(3) + 3 = 33 + 3 = 36 ✓
7) 10(7) + 2 = 70 + 2 = 72 ✓
8) 7(7) + 3 = 49 + 3 = 52 ✓
9) 6(2) + 5 = 12 + 5 = 17 ✓
10) 4(0.5) + 7 = 2 + 7 = 9 ✓
11) 8(0.5) + 11 = 4 + 11 = 15 ✓
12) 4(0.25) + 17 = 1 + 17 = 18 ✓

Section B:
1) 1 + 6(3) = 1 + 18 = 19 ✓
2) 9 + 7(3) = 9 + 21 = 30 ✓
3) 3 + 2(7) = 3 + 14 = 17 ✓
4) 11 + 5(12) = 11 + 60 = 71 ✓
5) 5 + 3(9) = 5 + 27 = 32 ✓
6) 4 + 5(8) = 4 + 40 = 44 ✓
7) 23 = 15 + 8 = 23 ✓
8) 28 = 3(9) + 1 = 27 + 1 = 28 ✓
9) 53 = 8(6) + 5 = 48 + 5 = 53 ✓
10) 13 = 11 + 4(0.5) = 11 + 2 = 13 ✓
11) 7 = 8(0.5) + 3 = 4 + 3 = 7 ✓
12) 12 = 7 + 15(1/3) = 7 + 5 = 12 ✓

Section C:
1) 4(8) - 1 = 32 - 1 = 31 ✓
2) 3(11) - 4 = 33 - 4 = 29 ✓
3) 6(6) - 5 = 36 - 5 = 31 ✓
4) 8(6) - 2 = 48 - 2 = 46 ✓
5) 2(14) - 7 = 28 - 7 = 21 ✓
6) 7(3) - 3 = 21 - 3 = 18 ✓
7) 9(4) - 4 = 36 - 4 = 32 ✓
8) 5(13) - 1 = 65 - 1 = 64 ✓
9) 12(4) - 9 = 48 - 9 = 39 ✓
10) 2(1.5) - 1 = 3 - 1 = 2 ✓
11) 4(4.5) - 8 = 18 - 8 = 10 ✓
12) 15(1/3) - 2 = 5 - 2 = 3 ✓

All answers verified!

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 = ½ (or 0.5)
11) x = ½ (or 0.5)
12) x = ¼ (or 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 = ½ (or 0.5)
11) x = ½ (or 0.5)
12) x = ⅓

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 = 3/2 (or 1.5)
11) x = 9/2 (or 4.5)
12) x = ⅓