Question

How do you solve `6abs(2x-4)=54`?

Answer 1

Divide both sides by `6`. Clear the absolute value sign by splitting the equation into two parts, one positive and one negative. Solve each for `x`.

Explanation:

`6abs(2x-4)=54`

Divide both sides by `6`.

`abs(2x-4)=9`

Clear the absolute value sign by splitting the equation into two parts, one positive and one negative.

`(2x-4)=9` and `-(2x-4)=9`

Positive Equation

`(2x-4)=9`

Add 4 to both sides.

`2x=9+4=13`

Divide both sides by `2`.

`x=13/2`

Negative Equation

`-(2x-4)=9` =

`-2x+4=9`

Subtract 4 from both sides.

`-2x=9-4=5`

Divide both sides by -2.

`x=-5/2`

`x=-5/2, 13/2`