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

May 27, 2018

$x = - \frac{100}{19} , \frac{284}{19}$

#### Explanation:

Solve:

$12 \left(16\right) = \left\mid 19 x - 92 \right\mid$

Simplify $12 \left(16\right)$ to $192$

$192 = \left\mid 19 x - 92 \right\mid$

Switch sides.

$\left\mid 19 x - 92 \right\mid = 192$

Since $\left\mid a \right\mid = a$ and $\left\mid - a \right\mid = a$, we need to break down the equation into positive and negative equations.

$19 x - 92 = 192$ and $- \left(19 x - 92\right) = 192$

Positive equation

$19 x - 92 = 192$

Add $92$ to both sides.

$19 x = 192 + 92$

$19 x = 284$

Divide both sides by $19$.

$x = \frac{284}{19}$

Negative equation

$- \left(19 x - 92\right) = 192$

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

$- 19 x + 92 = 192$

Subtract $92$ from both sides.

$- 19 x = 192 - 92$

$- 19 x = 100$

Divide both sides by $- 19$.

$x = - \frac{100}{19}$

Solutions for $x$.

$x = - \frac{100}{19} , \frac{284}{19}$