Question

How do you solve `| 2x - 5 | + 3 = 12`?

Answer 1

`x = 7, -2`

Explanation:

`|2x - 5| + 3 = 12` Given Equation

`|2x - 5| = 9` Subtracted `3` from both sides

`|2x| = 14` Added `5` to each side.

`x = 7` Divided 2 by both sides

Since this is absolute value, you are also required to also solve the equation where in this case `x` could also be negative aswell as positive.

`-|2x - 5| + 3 = 12`

`-2x + 5 + 3 = 12` Distributed the negative sign.

`-2x + 8 = 12` Added 5 and 3.

`-2x = 4` Subtracted 8 from 12.

`x = -2` Divided -2 to 4.

Answer 2

`x=-2,7`

Explanation:

Solve:

`abs(2x-5)+3=12`

Since `abs(a)=a and -a`, the equation can be broken into two equations:

`2x-5+3=12` and `-(2x-5)+3=12`

Solve the first equation:

`2x-5+3=12`

Simplify `(-5+3)` to `-2`.

`2x-2=12`

Add `2` to both sides of the equation.

`2x=12+2`

Simplify.

`2x=14`

Divide both sides by `2`.

`x=14/2`

`x=7`

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Solve the second equation:

`-(2x-5)+3=12`

Expand.

`-2x+5+3=12`

Simplify `(5+3)` to `8`.

`-2x+8=12`

Subtract `8` from `12`

`-2x=12-8`

Simplify.

`-2x=4`

Divide both sides by `-2`.

`x=4/(-2)`

`x=-2`

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`x=-2,7`