# Solving Linear Equations in One Variable

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```							Solving Linear Equations in One Variable                                    Sept 09, 2009

Examples:                                                                   Check Solutions

1.      3x  5  1                                                          3( 2 )  5  1
3x  6         Add 5 to both sides of the equation                  6  5  1
x  2         Divide both sides of equation by 3                        1 1 

2.     5x  1  x  7
4x  1  7          Subtract x from both sides of equation
4x  8         Add 1 to both sides of equation
x  2          Divide both sides of equation by 4

3.      4 x  1  2( 2 x  3 )
4 x  1  4 x  6 Distribute by multiplying 2 into parenthesis
1  6       Subtract 4x from both sides of equation
No Solution     Variables disappear leaving false statement

4.     3( x  5 )  3 x  15
3 x  15  3 x  15      Distribute by multiplying 3 into parenthesis
15  15           Subtract 3x from both sides of equation
Infinite Solutions         Variables disappear leaving true statement

x   3x
5.             2
3   4

 x   3x    
12         2      Clear fractions by multiplying equation by LCD
 3    4    

4 x  9 x  24      Distribute by multiplying 12 into parenthesis

13 x  24      Combine like terms
24
x          Divide both sides of the equation by 13
13

```
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