Question

How do you solve `12(16) = abs(19x-92)`?

Answer 1

`x=-100/19,284/19`

Explanation:

Solve:

`12(16)=abs(19x-92)`

Simplify `12(16)` to `192`

`192=abs(19x-92)`

Switch sides.

`abs(19x-92)=192`

Since `absa=a` and `abs(-a)=a`, we need to break down the equation into positive and negative equations.

`19x-92=192` and `-(19x-92)=192`

Positive equation

`19x-92=192`

Add `92` to both sides.

`19x=192+92`

`19x=284`

Divide both sides by `19`.

`x=284/19`

Negative equation

`-(19x-92)=192`

Distribute the `-1` on the left-hand side.

`-19x+92=192`

Subtract `92` from both sides.

`-19x=192-92`

`-19x=100`

Divide both sides by `-19`.

`x=-100/19`

Solutions for `x`.

`x=-100/19,284/19`