The value of x is [tex]-\frac{42}{13}[/tex]
Step-by-step explanation:
The expression is [tex]\frac{4}{3} (\frac{2x}{3} +\frac{1}{2} )=\frac{x}{6} -\frac{5}{3}[/tex]
To find the value of x, we need to simplify the equation,
Multiply the term [tex](\frac{2x}{3} +\frac{1}{2} )[/tex] by [tex]\frac{4}{3}[/tex],
[tex]\frac{8x}{9} +\frac{4}{6} =\frac{x}{6}-\frac{5}{3}[/tex]
Subtracting by [tex]\frac{x}{6}[/tex] and [tex]\frac{4}{6}[/tex] on both sides of the equation, we get,
[tex]\frac{8x}{9} -\frac{x}{6} =-\frac{5}{3}-\frac{4}{6}[/tex]
Taking LCM on both sides,
[tex]\frac{48x-9x}{54} =\frac{-10-4}{6}[/tex]
Simplifying, we get,
[tex]\frac{39x}{54} =-\frac{14}{6}[/tex]
Multiplying both sides by 54,
[tex]39x=\frac{-14(54)}{6} \\39x=-14(9)\\39x=-126[/tex]
Dividing both sides by 39, we get,
[tex]x=-\frac{42}{13}[/tex]
Thus, the value of x is [tex]-\frac{42}{13}[/tex]
