Multi-Step Equation Notes and Worksheets - Lindsay Bowden - Free Printable

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

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## ✔ Reminders Section

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

> *Explanation:* The goal of solving any equation is to find the value of the unknown (variable, usually ‘x’). To do this, we manipulate the equation so that the variable stands alone on one side, with a number on the other.

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

> *Explanation:* This is the Balance Principle — equations are like scales. Whatever you add, subtract, multiply, or divide on one side, you must do to the other to keep the equation balanced and true.

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## ✔ Steps Section

1. _Simplify_ each side
- combine like terms
- distribute

> *Explanation:* Before moving variables or constants, simplify both sides as much as possible. Use the distributive property if needed, and combine any like terms (e.g., 3x + 2x = 5x).

2. If there are variables on both sides, move them to the _left_ side

> *Note:* While “left” is common convention, technically you can move them to *either* side — but left is standard for consistency. You want all variable terms on one side, constants on the other.

3. If there are constants on both sides, move them all to the _right_ side

> *Explanation:* After getting variables on one side, move all numbers (constants) to the opposite side using inverse operations.

4. Use the inverse operation(s) to _isolate_ the variable

> *Explanation:* Once the variable is alone on one side with its coefficient, use division or multiplication (inverse of multiplication or division) to get the variable by itself (coefficient = 1).

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## ✔ Examples – Solved Step-by-Step

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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 (to move constant to right)
→ `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
→ `(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: Subtract 2x from both sides (move variable terms to left)
→ `6x - 2x - 4 = 16`
→ `4x - 4 = 16`

Step 2: Add 4 to both sides (move constants to right)
→ `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: `½(8x + 4) = 2x + 10`

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

Step 2: Subtract 2x from both sides (move variables to left)
→ `4x - 2x + 2 = 10`
→ `2x + 2 = 10`

Step 3: Subtract 2 from both sides (move constants to right)
→ `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 Notes Sheet:

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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

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

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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 practice more problems or need a printable version! 😊