Linear equations

RECIPE TO SOLVE A LINEAR EQUATION

1. Remove the parenthesis, brackets,..

2. Remove the denominators.

3. Take the terms with variables to one side and the numerical ones to the other.

4. Reduce like terms.

5. Work out the “x” and calculate the solution.

6. CHECK THE SOLUTION

EXAMPLES

Example 1:     3·(x + 2) = 9

Remove the parenthesis by doing the distributive property               3x + 6 = 9

Take the variables..        3x = 9 – 6

Reduce . .                3x = 3

Work out . . .    


Check …      3·(1 + 2) = 9;        3·3 = 9;         9 = 9

Example 2:  x + 5 – 2x = 3·(x + 1) -18

Remove ..    x + 5 – 2x = 3x + 3 - 18

Take the variables..    x – 2x – 3x = 3 – 18 - 5

Reduce . .         x – 5x = 3 – 23                  -4x = -20

Work out . . .        


Check …      5 + 5 – 2·5 = 3·(5 + 1) – 18
                     10 – 10 = 3·6 – 18
                   0 = 18 – 18                        0 = 0     

Example 3:

 

Example 4:

 

Example 5:

 

Example 6:

 

 

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Exercise: solve the following equations: