Solving Equations

To solve equations we use inverses (do the opposite) to find out what the unknown is

One step equations

Examples:

1)        2x = 8              We divide both sides by 2 to get x on its own
             x = 4

2)      x + 5 = 9           We subtract 5 from both sides
               x = 4

3)     x - 2 = 12            We add 2 to both sides
             x = 14

Two step equations

Examples:

1)      2x + 1 = 5           First we subtract 1 to get 2x on its own
                      2x = 4          Then we divide both sides by 2 to get x
                 x = 2

2)       3x - 5 = 16         Add 5 to both sides
               3x =  21        Divide both sides by 3
                 x = 7

3)       7 - 4x = 3           Because we have a minus 4x we add this first 
                 7 = 3 + 4x   Now subtract 3
                 4 = 4x         Divide both sides by 4
                 x = 1

Unknowns on both sides

Examples
  
1)       2x + 3 = x + 5     Deal with the smallest x in this case x on the RHS
           x  + 3 = 5            Now continue as above
                 x = 2

2)      3x - 7 = 5x + 9     Be careful with negatives
              -7 = 2x + 9
             -16 = 2x    
              - 8 = x

Equations with Brackets

First multiply out the brackets then continue as above
Examples

1)      3(2x + 5) = 33
            6x + 15 =  33
                    6x = 18
                     x = 3

2)    2(x  + 7) = 3(2x - 2)
        2x  + 14 = 6x - 6
                 14 = 4x - 6
                 20 = 4x
                  5 = x