Question

How do you solve `2abs(3x - 4) + 8=6`?

Answer 1

Solve as you would any equation, then make `|3x-4|` positive, `3x-4=-1`, and negative, `-(3x-4)=-1`. Solve for `x`.

Explanation:

`2|3x-4|+8=6`

Subtract `8` from both sides.

`2|3x-4|=-2`

Divide both sides by `2`.

`|3x-4|=-1`

The quantity inside the absolute value symbols can be positive or negative: `3x-4=-1` and `-(3x-4)=-1`

When `|3x-4|` is positive:

`3x-4=-1`

Add `4` to both sides of the equation.

`3x=3`

Divide both sides by `3`.

`x=1`

When `|3x-4|` is negative:

`-(3x-4)=-1`

`-3x+4=-1`

Subtract `4` from both sides.

`-3x=-5`

Divide both sides by `-3`.

`x=5/3`

Answer: `x=1,5/3`