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

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

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## ✔ Reminders:

1. 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. We do this by getting the variable alone on one side of the equals sign.

2. If you do something to one side of an equation, you must: _do the same thing to the other side_
→ This maintains the balance of the equation. It’s the “Golden Rule” of algebra!

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## ✔ Steps:

1. _Simplify_ each side
• combine like terms
• distribute
→ First, clean up each side as much as possible using arithmetic and distribution.

2. If there are variables on both sides, move them to the _left_ side
→ Conventionally, we collect all variable terms on the left side (though right side works too — consistency helps!).

3. If there are constants on both sides, move them all to the _right_ side
→ Again, convention: constants go to the right, variables to the left.

4. Use the inverse operation(s) to _isolate_ the variable
→ Undo operations (add/subtract, multiply/divide) to get the variable alone.

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## ✔ 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 subtracting 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 on left side
→ (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 left, constants to right. Subtract 2x from both sides
→ 6x − 2x − 4 = 16
→ 4x − 4 = 16

Step 2: Add 4 to both sides
→ 4x = 16 + 4
→ 4x = 20

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

✔ Answer: x = 5

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Example 4:  (1/2)(8x + 4) = 2x + 10

Step 1: Distribute 1/2 on the left side
→ (1/2)·8x + (1/2)·4 = 2x + 10
→ 4x + 2 = 2x + 10

Step 2: Subtract 2x from both sides
→ 4x − 2x + 2 = 10
→ 2x + 2 = 10

Step 3: Subtract 2 from both sides
→ 2x = 10 − 2
→ 2x = 8

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

✔ Answer: x = 4

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## 📝 Final Completed Worksheet:

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

Steps:

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

Examples:

1. x = 7
2. x = 5
3. x = 5
4. x = 4

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Let me know if you’d like a printable version or practice problems! 😊