Question

How do you solve `abs(6x+7)=5x+2`?

Answer 1

`x=-9/11`

The absolute value operation does:

1 - If the inner value of absolute value is non-negative, it returns the value.

2- If the inner value of absolute value is negative, it returns `(-1)` times of the value.

Our given equality is:

`abs(6x+7)=5x+2`

• If `6x+7 >=0` then absolute value opeariton will return `6x+7`

`6x+7=5x+2`
`x=-5`

There is an important trick when it comes to absolute value operation. Always test the result with the if condition.

`6*(-5)+7>=0` fails. So `-5` is not in the solution set.

• If `6x+7<0` then absolute value opeariton will return `-(6x+7)`

`-6x-7 = 5x+2`
`-9=11x`
`-9/11=x`

Again, lets test the if condition.

`6*(-9/11)+7<0` success!

So `x=-9/11`