Answer:
[tex]\boxed {x = -75}[/tex]
Step-by-step explanation:
Solve for the value of [tex]x[/tex]:
[tex]\frac{1}{3}x + 2 = \frac{1}{5}x - 8[/tex]
-Take [tex]\frac{1}{5}x[/tex] and subtract it from [tex]\frac{1}{3}x[/tex]:
[tex]\frac{1}{3}x + 2 - \frac{1}{5}x = \frac{1}{5}x - \frac{1}{5}x - 8[/tex]
[tex]\frac{2}{15}x + 2 = -8[/tex]
-Subtract [tex]2[/tex] to both sides:
[tex]\frac{2}{15}x + 2 - 2 = -8 - 2[/tex]
[tex]\frac{2}{15}x = -10[/tex]
-Multiply both sides by [tex]\frac{15}{2}[/tex], which is the reciprocal of [tex]\frac{2}{15}[/tex].
[tex]x = -10 \times (\frac{15}{2})[/tex]
[tex]x = \frac{-10 \times 15}{2}[/tex]
[tex]x = \frac{-150}{2}[/tex]
-Divide [tex]-150[/tex] by [tex]2[/tex]:
[tex]x = \frac{-150}{2}[/tex]
[tex]\boxed {x = -75}[/tex]
So, the value of [tex]x[/tex] is [tex]-75[/tex].
