# How do you solve the equation 2/3abs(5-2x)-1/2=5?

Jun 26, 2017

Solution : $x = 6 \frac{5}{8} , x = - 1 \frac{5}{8}$

#### Explanation:

$\frac{2}{3} | 5 - 2 x | - \frac{1}{2} = 5 \mathmr{and} \frac{2}{3} | 5 - 2 x | = 5 + \frac{1}{2}$ or

$\frac{2}{3} | 5 - 2 x | = \frac{11}{2} \mathmr{and} | 5 - 2 x | = \frac{3}{2} \cdot \frac{11}{2}$ or

$| 5 - 2 x | = \frac{33}{4} \mathmr{and} 5 - 2 x = \frac{33}{4} \mathmr{and} 2 x = 5 - \frac{33}{4}$ or

$2 x = - \frac{13}{4} \mathmr{and} x = - \frac{13}{8} \mathmr{and} x = - 1 \frac{5}{8}$ OR

$| 5 - 2 x | = \frac{33}{4} \mathmr{and} 5 - 2 x = - \frac{33}{4} \mathmr{and} 2 x = 5 + \frac{33}{4}$ or

$2 x = \frac{53}{4} \mathmr{and} x = \frac{53}{8} \mathmr{and} x = 6 \frac{5}{8}$

Solution : $x = 6 \frac{5}{8} , x = - 1 \frac{5}{8}$ [Ans]