Worksheet for solving multi-step equations with examples and guided steps.

Absolutely! Let’s fill in the blanks and solve each example step-by-step.

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## ✔ Reminders:

- Solving an equation means to _isolate_ the variable (or get the variable _by itself_)

→ The goal is to find the value of the variable that makes the equation true. That means getting the variable alone on one side of the equals sign.

- If you do something to one side of an equation, you must: _do the same thing to the other side_

→ This keeps the equation balanced — like a scale. Whatever you add, subtract, multiply, or divide on one side, you must do to the other.

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## ✔ Steps:

1. _Simplify_ each side
• combine like terms
• distribute

2. If there are variables on both sides, move them to the _same_ side
→ Usually we pick the side with the larger coefficient to avoid negative numbers, but “same side” just means consolidate all variable terms together.

3. If there are constants on both sides, move them all to the _opposite_ side
→ So if variables are on the left, move constants to the right (and vice versa).

4. Use the inverse operation(s) to _isolate_ the variable
→ Undo operations using their opposites (e.g., undo +5 by subtracting 5; undo ×3 by ÷3).

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# 📌 Now let’s solve the examples:

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Example 1: 3(x – 5) = 6

Step 1: Distribute
→ 3·x – 3·5 = 6
→ 3x – 15 = 6

Step 2: Add 15 to both sides (inverse of -15)
→ 3x = 6 + 15
→ 3x = 21

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

✔ Answer: x = 7

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Example 2: 4x + 2x – 5 = 25

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

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

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

✔ Answer: x = 5

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Example 3: 6x – 4 = 2x + 16

Step 1: Move 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 = 16 + 4
→ 4x = 20

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

✔ Answer: x = 5

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Example 4: ½(8x + 4) = 2x + 10

Step 1: Distribute ½
→ 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 to the other side
Subtract 2 from both sides:
→ 2x = 10 – 2
→ 2x = 8

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

✔ Answer: x = 4

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## ✍️ Final Filled Worksheet Summary:

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Reminders:

- Solving an equation means to isolate the variable (or get the variable by itself)
- If you do something to one side of an equation, you must: do the same thing to the other side

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Steps:

1. Simplify each side
• combine like terms
• distribute
2. If there are variables on both sides, move them to the same side
3. If there are constants on both sides, move them all to the opposite side
4. Use the inverse operation(s) to isolate the variable

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Examples:

1. 3(x – 5) = 6 → x = 7
2. 4x + 2x – 5 = 25 → x = 5
3. 6x – 4 = 2x + 16 → x = 5
4. ½(8x + 4) = 2x + 10 → x = 4

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Let me know if you’d like to see these solved with visual steps or want practice problems! 😊