Question

How do you solve `abs(2x+3)+4=5x`?

Answer 1

`x=1/7,7/3`

Refer to the explanation for the process.

Explanation:

Solve:

`abs(2x+3)+4=5x`

Since `absa=a` and `abs(-a)=a`, there is both a positive and negative component to the equation, therefore you will have two equations to solve.

First Equation: (2x+3) is Positive

`2x+3+4=5x`

Subtract `2x` from both sides.

`3+4=5x-2x`

Simplify.

`7=3x`

Divide both sides by `3`.

`7/3=x`

Switch sides.

`x=7/3`

Second Equation: (2+3) is Negative

`-(2x+3)+4=5x`

Simplify.

`-2x-3+4=5x`

Add `2x` to both sides.

`-3+4=5x+2x`

Simplify.

`1=7x`

Divide both sides by `7`.

`1/7=x`

Switch sides.

`x=1/7`

Therefore:

`x=1/7,7/3`