we are trying to solve an Absolute Value Equation that has a fraction. It is 2x over 5 = 8.

x = 20 or x = -20
Explanations:The given equation is:
[tex]|\frac{2x}{5}|\text{ = 8}[/tex]The equation will be splitted into two and solve differently
[tex]\begin{gathered} \frac{2x}{5}=\text{ 8} \\ \text{and }\frac{2x}{5}=-8 \end{gathered}[/tex]For 2x/5 =8
Cross multiply
2x = 8(5)
2x = 40
x = 40/2
x = 20
For 2x/5 = -8
Cross multiply
2x = -8(5)
2x = -40
x = -40/2
x = -20
x = 20 or x = -20