# How do you solve 6abs(2x-4)=54?

Jul 4, 2015

Divide both sides by $6$. Clear the absolute value sign by splitting the equation into two parts, one positive and one negative. Solve each for $x$.

#### Explanation:

$6 \left\mid 2 x - 4 \right\mid = 54$

Divide both sides by $6$.

$\left\mid 2 x - 4 \right\mid = 9$

Clear the absolute value sign by splitting the equation into two parts, one positive and one negative.

$\left(2 x - 4\right) = 9$ and $- \left(2 x - 4\right) = 9$

Positive Equation

$\left(2 x - 4\right) = 9$

$2 x = 9 + 4 = 13$

Divide both sides by $2$.

$x = \frac{13}{2}$

Negative Equation

$- \left(2 x - 4\right) = 9$ =

$- 2 x + 4 = 9$

Subtract 4 from both sides.

$- 2 x = 9 - 4 = 5$

Divide both sides by -2.

$x = - \frac{5}{2}$

$x = - \frac{5}{2} , \frac{13}{2}$