Linear Equations with Parentheses

Article Contents

1. When Equations Have Parentheses
2. Step 1: Expand the Parentheses
3. Step 2: Collect Like Terms
4. Step 3: Solve
5. Examples

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1. When Equations Have Parentheses {#when-equations-have-parentheses}

Some equations have parentheses that need to be removed before solving.

Example: $2(x+3)=14$

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2. Step 1: Expand the Parentheses {#step-1-expand-the-parentheses}

Use the distributive property:

$$a(b+c)=ab+ac$$

Example

$2(x+3)=14$ becomes:

$$2x+6=14$$

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3. Step 2: Collect Like Terms {#step-2-collect-like-terms}

Group all $x$ terms together, all numbers together.

Example

$2x+6=14$:

• Keep $2x$ on the left
• Move 6 to the right side (subtract 6):
  
  $$2x=14-6$$
  
  
  $$2x=8$$

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4. Step 3: Solve {#step-3-solve}

Divide both sides by the coefficient:

$$2x=8\Rightarrow x=8/2=4$$

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5. Examples {#examples}

Example 1

Solve: $3(x+2)=21$

```

Step 1: 3(x + 2) = 3x + 6

Step 2: 3x + 6 = 21

Step 3: 3x = 21 - 6 = 15

Step 4: x = 15/3 = 5

```

Check: $3(5+2)=3(7)=21✓$

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Example 2

Solve: $2(x+1)=x+7$

```

Step 1: 2x + 2 = x + 7

Step 2: 2x - x = 7 - 2 (subtract x, subtract 2)

Step 3: x = 5

```

Check: $2(5+1)=2(6)=12=5+7✓$

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Example 3

Solve: $4(x-3)=2x+6$

```

Step 1: 4x - 12 = 2x + 6

Step 2: 4x - 2x = 6 + 12 (subtract 2x, add 12)

Step 3: 2x = 18

Step 4: x = 9

```

Check: $4(9-3)=4(6)=24=2(9)+6=18+6✓$

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Interactive Exercises

• Equations with Plus - Practice equations with parentheses on both sides

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Related Articles

• Comprehensive Guide - Full solving techniques
• Simple Equations - Basic equations