Question

How do you solve the equation `abs(9x-2)=7`?

Answer 1

`x=1, -5/9`

Explanation:

Consider `absx=3`. `x` can be 3 but it can also be `-3`. And so when evaluating absolute value questions, we need to evaluate positive and negative values.

Positive

`abs(9x-2)=7`

`9x-2=7`

`9x=9`

`x=1`

Negative

`abs(9x-2)=7`

`-(9x-2)=7`

`-9x+2=7`

`-9x=5`

`x=-5/9`

and we can see this on the graph:

graph{(y-abs(9x-2))(y-0x-7)=0 [-9.58, 10.42, -0.96, 9.04]}