Worksheet for solving multi-step equations, including reminders, steps, and four example problems.

Let’s solve each equation step by step. We’ll follow the rules for solving multi-step equations: simplify first, move variables to one side and constants to the other, then use inverse operations to isolate the variable.

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Problem 1: 3(x – 5) = 6

Step 1: Distribute the 3 on the left side.
→ 3·x – 3·5 = 6 → 3x – 15 = 6

Step 2: Add 15 to both sides to move the constant.
→ 3x – 15 + 15 = 6 + 15 → 3x = 21

Step 3: Divide both sides by 3 to isolate x.
→ 3x ÷ 3 = 21 ÷ 3 → x = 7

✔ Check: Plug x = 7 back in: 3(7 – 5) = 3(2) = 6 ✔️

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Problem 2: 4x + 2x – 5 = 25

Step 1: Combine like terms on the left (4x + 2x).
→ 6x – 5 = 25

Step 2: Add 5 to both sides.
→ 6x – 5 + 5 = 25 + 5 → 6x = 30

Step 3: Divide both sides by 6.
→ 6x ÷ 6 = 30 ÷ 6 → x = 5

✔ Check: 4(5) + 2(5) – 5 = 20 + 10 – 5 = 25 ✔️

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Problem 3: 6x – 4 = 2x + 16

Step 1: Move all variables to one side. Subtract 2x from both sides.
→ 6x – 2x – 4 = 16 → 4x – 4 = 16

Step 2: Move constants to the other side. Add 4 to both sides.
→ 4x – 4 + 4 = 16 + 4 → 4x = 20

Step 3: Divide both sides by 4.
→ 4x ÷ 4 = 20 ÷ 4 → x = 5

✔ Check: Left: 6(5) – 4 = 30 – 4 = 26; Right: 2(5) + 16 = 10 + 16 = 26 ✔️

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Problem 4: ½(8x + 4) = 2x + 10

Step 1: Distribute the ½ on the left.
→ ½·8x + ½·4 = 2x + 10 → 4x + 2 = 2x + 10

Step 2: Move variables to one side. Subtract 2x from both sides.
→ 4x – 2x + 2 = 10 → 2x + 2 = 10

Step 3: Move constants. Subtract 2 from both sides.
→ 2x + 2 – 2 = 10 – 2 → 2x = 8

Step 4: Divide by 2.
→ 2x ÷ 2 = 8 ÷ 2 → x = 4

✔ Check: Left: ½(8·4 + 4) = ½(32 + 4) = ½(36) = 18; Right: 2(4) + 10 = 8 + 10 = 18 ✔️

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Final Answer:
1. x = 7
2. x = 5
3. x = 5
4. x = 4