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

Mar 3, 2018

$x = 7 , - 2$

#### Explanation:

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

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

$| 2 x | = 14$ 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.

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

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

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

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

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

Mar 3, 2018

$x = - 2 , 7$

#### Explanation:

Solve:

$\left\mid 2 x - 5 \right\mid + 3 = 12$

Since $\left\mid a \right\mid = a \mathmr{and} - a$, the equation can be broken into two equations:

$2 x - 5 + 3 = 12$ and $- \left(2 x - 5\right) + 3 = 12$

Solve the first equation:

$2 x - 5 + 3 = 12$

Simplify $\left(- 5 + 3\right)$ to $- 2$.

$2 x - 2 = 12$

Add $2$ to both sides of the equation.

$2 x = 12 + 2$

Simplify.

$2 x = 14$

Divide both sides by $2$.

$x = \frac{14}{2}$

$x = 7$

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Solve the second equation:

$- \left(2 x - 5\right) + 3 = 12$

Expand.

$- 2 x + 5 + 3 = 12$

Simplify $\left(5 + 3\right)$ to $8$.

$- 2 x + 8 = 12$

Subtract $8$ from $12$

$- 2 x = 12 - 8$

Simplify.

$- 2 x = 4$

Divide both sides by $- 2$.

$x = \frac{4}{- 2}$

$x = - 2$

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$x = - 2 , 7$