Linear Equations with Parentheses

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

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

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

Example:

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

Use the distributive property:

Example

becomes:

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

Group all terms together, all numbers together.

Example

:
  • Keep on the left
  • Move 6 to the right side (subtract 6):

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

Divide both sides by the coefficient:

5. Examples {#examples}

Example 1

Solve: 

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:

Example 2

Solve: 

Step 1: 2x + 2 = x + 7
Step 2: 2x - x = 7 - 2    (subtract x, subtract 2)
Step 3: x = 5

Check:

Example 3

Solve: 

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:

Interactive Exercises