Linear Equations Worksheet featuring eight algebraic equations to solve, designed for math practice.

Let’s solve each equation one by one, step by step. I’ll show all the work so you can follow along easily.

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Problem ①: 8(4a - 4) - 1 = 14 - 8a

Step 1: Distribute the 8 on the left side
→ 32a - 32 - 1 = 14 - 8a
→ 32a - 33 = 14 - 8a

Step 2: Add 8a to both sides to get all “a” terms on one side
→ 32a + 8a - 33 = 14
→ 40a - 33 = 14

Step 3: Add 33 to both sides
→ 40a = 14 + 33
→ 40a = 47

Step 4: Divide both sides by 40
→ a = 47/40

✔ Final Answer for ①: a = 47/40

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Problem ②: 4(-8x + 5) = -30x - 26

Step 1: Distribute the 4 on the left
→ -32x + 20 = -30x - 26

Step 2: Add 32x to both sides
→ 20 = 2x - 26

Step 3: Add 26 to both sides
→ 46 = 2x

Step 4: Divide by 2
→ x = 23

✔ Final Answer for ②: x = 23

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Problem ③: 27 = 46 + 3x - x

Step 1: Combine like terms on the right (3x - x = 2x)
→ 27 = 46 + 2x

Step 2: Subtract 46 from both sides
→ 27 - 46 = 2x
→ -19 = 2x

Step 3: Divide by 2
→ x = -19/2

✔ Final Answer for ③: x = -19/2

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Problem ④: 38 + 7k = 8(k + 4)

Step 1: Distribute the 8 on the right
→ 38 + 7k = 8k + 32

Step 2: Subtract 7k from both sides
→ 38 = k + 32

Step 3: Subtract 32 from both sides
→ 6 = k

✔ Final Answer for ④: k = 6

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Problem ⑤: -2(4 - x) = 6(x + 4) + 4x

Step 1: Distribute on both sides
Left: -8 + 2x
Right: 6x + 24 + 4x → combine to 10x + 24
So: -8 + 2x = 10x + 24

Step 2: Subtract 2x from both sides
→ -8 = 8x + 24

Step 3: Subtract 24 from both sides
→ -32 = 8x

Step 4: Divide by 8
→ x = -4

✔ Final Answer for ⑤: x = -4

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Problem ⑥: 0.05z + 0.2 = 0.15z - 10.5

Step 1: Subtract 0.05z from both sides
→ 0.2 = 0.10z - 10.5

Step 2: Add 10.5 to both sides
→ 10.7 = 0.10z

Step 3: Divide by 0.10 (or multiply by 10)
→ z = 107

✔ Final Answer for ⑥: z = 107

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Problem ⑦: 4(6 + 4x) = 0

Step 1: Distribute the 4
→ 24 + 16x = 0

Step 2: Subtract 24 from both sides
→ 16x = -24

Step 3: Divide by 16
→ x = -24/16 → simplify by dividing numerator and denominator by 8
→ x = -3/2

✔ Final Answer for ⑦: x = -3/2

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Problem ⑧: x/8 - x/9 = 1

Step 1: Find common denominator of 8 and 9 → it’s 72
Rewrite fractions:
→ (9x)/72 - (8x)/72 = 1
→ (9x - 8x)/72 = 1
→ x/72 = 1

Step 2: Multiply both sides by 72
→ x = 72

✔ Final Answer for ⑧: x = 72

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Final Answer:
① a = 47/40
② x = 23
③ x = -19/2
④ k = 6
⑤ x = -4
⑥ z = 107
⑦ x = -3/2
⑧ x = 72