Question

How do you solve `3|2x + -5| + 3 = 42`?

Answer 1

`x=9 or x=-4`

Explanation:

Here, `3|2x+(-5)|+3=42,`

Adding `(-3)` both sides

`3|2x+(-5)|+3+(-3)=42+(-3)`

`=>3|2x+(-5)|=39,`

Dividing both sides by 3

`(cancel(3)|2x+(-5)|)/(cancel(3))=39/3=>|2x+(-5)|=13`

`2x+(-5)=13or2x+(-5)=-13`

Adding `5` both sides

`2x+(-5)+5=13+5or2x+(-5)+5=-13+5`

`=>2x=18 or 2x=-8=>x=9 or x=-4`

Answer 2

`x=-4,9`

Explanation:

Solve:

`3abs(2x+ -5)+3=42`

Simplify the absolute value.

`3abs(2x-5)+3=42`

Subtract `3` from both sides of the equation.

`3abs(2x-5)+3-3=42-3`

Simplify.

`3abs(2x-5)+0=39`

`3abs(2x-5)=39`

Divide both sides by `3`.

`(cancel(3)^1abs(2x-5))/cancel(3)^1=cancel39^13/cancel(3)^1`

Simplify.

`abs(2x-5)=13`

Since `abs(+-a)=a`, we can break the equation into two equations:

`2x-5=13` and `-(2x-5)=13`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve the first equation:

Add `5` to both sides of the equation.

`2x-5+5=13+5`

Simplify.

`2x=18`

Divide both sides by `2`.

`(cancel(2)^1x)/cancel(2)^1=cancel18^9/cancel2^1`

Simplify.

`x=9`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve the second equation:

`-(2x-5)=13`

Expand.

`-2x+5=13`

Subtract `5` from both sides.

`-2x+5-5=13-5`

Simplify.

`-2x+0=8`

`-2x=8`

Divide both sides by `-2`.

`(cancel(-2)^1x)/(cancel(-2)^1)=cancel8^4/(cancel(-2)^1`

Simplify.

`x=-4`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`x=-4,9`