What is the answer to |5x-9|>7

Question

The question asks Solve for x.

Answer 1

|5x-9|>7

 

Either:    (5x-9)>7         or          -(5x-9)>7

              5x > 16          or          -5x+9>7

               x>16/5         or           -5x>-2

                                                  5x<2      [multiply by (-1) reverses sense of inequality]

               x > 16/5      OR           x < 5/2

 

Check:

  Test value for x>16/5:  x=10

                        |5(10)-9|>7   ?

                        |41|>7   ?

                         41>7   ?yes

  Test value for x<5/2:  x=0

                      |5(0)-9|>7   ?

                            |-9|>7   ?

                               9>7   ?yes

Answer 2

Delaney,

 

Here is an easy way to do absolute values!

 

|5x - 9| > 7

 

-7 > 5x - 9 > 7

 

Either split into two problems or work as one!

 

add 9 to all three sections, resulting in:

 

 2 > 5x > 16

 

divide all by 5

 

 2/5 > x > 16/5

 

Therefore: x > 16/5 and x < 2/5