Answer:
[tex]\boxed {x = \frac{7}{10}}[/tex]
Step-by-step explanation:
Solve for the value of [tex]x[/tex]:
[tex]\frac{2}{3}(3x - 4) + 3x = \frac{5}{6}[/tex]
-Use Distributive Property:
[tex]\frac{2}{3}(3x - 4) + 3x = \frac{5}{6}[/tex]
[tex]2x - \frac{8}{3} + 3x = \frac{5}{6}[/tex]
-Combine like terms:
[tex]2x - \frac{8}{3} + 3x = \frac{5}{6}[/tex]
[tex]5x - \frac{8}{3} = \frac{5}{6}[/tex]
-Add [tex]\frac{8}{3}[/tex] on both sides and the least common multiple of both [tex]6[/tex] and [tex]3[/tex] is [tex]6[/tex]. So, convert both fractions [tex]\frac{5}{6}[/tex] and [tex]\frac{8}{3}[/tex] with the denominator [tex]6[/tex]:
[tex]5x - \frac{8}{3} + \frac{8}{3} = \frac{5}{6} + \frac{8}{3}[/tex]
[tex]5x = \frac{5}{6} + \frac{16}{6}[/tex]
-Since both fractions have the same denominators, you add them adding the numerators together:
[tex]5x = \frac{5 + 16}{6}[/tex]
[tex]5x = \frac{21}{6}[/tex]
-Reduce the fraction to the lowest term by extracting and canceling out the [tex]3[/tex]:
[tex]5x = \frac{21}{6}[/tex]
[tex]5x = \frac{7}{2}[/tex]
-Divide [tex]5[/tex] on both sides of the equation. But instead of dividing it, you multiply the denominator [tex]2[/tex] by [tex]5[/tex]:
[tex]\frac{5x}{5} = \frac{\frac{7}{2} }{5}[/tex]
[tex]x = \frac{7}{2 \times 5}[/tex]
[tex]\boxed {x = \frac{7}{10}}[/tex]
So, therefore, the value of [tex]x[/tex] is [tex]\frac{7}{10}[/tex].
