Answer
{$-\frac{2}{7}$}
Work Step by Step
Step 1: $\frac{5}{6}x-2x+\frac{4}{3}=\frac{5}{3}$
Step 2: Multiplying both sides by 6, the LCD of the fractions:
$6(\frac{5}{6}x-2x+\frac{4}{3})=6(\frac{5}{3})$
Step 3: $6(\frac{5}{6}x)-6(2x)+6(\frac{4}{3})=6(\frac{5}{3})$
Step 4: $5x-12x+8=10$
Step 5: $-7x+8=10$
Step 6: Subtracting 8 from both sides, $-7x+8-8=10-8$
Step 7: $-7x=2$
Step 8: Dividing both sides by $-7$,
$\frac{-7x}{-7}=\frac{2}{-7}$
Step 9: $x=-\frac{2}{7}$
Check:
Step 1: Substituting the answer in the initial equation,
$\frac{5}{6}(-\frac{2}{7})-2(-\frac{2}{7})+\frac{4}{3}=\frac{5}{3}$
Step 2: $(-\frac{10}{42})+\frac{4}{7}+\frac{4}{3}=\frac{5}{3}$
Step 3: $(-\frac{5}{21})+\frac{4}{7}+\frac{4}{3}=\frac{5}{3}$
Step 4: $\frac{-5+4(3)+7(4)}{21}=\frac{5}{3}$
Step 5: $\frac{-5+12+28}{21}=\frac{5}{3}$
Step 6: $\frac{35}{21}=\frac{5}{3}$
Step 7: $\frac{5}{3}=\frac{5}{3}$
Since the solution checks, the solution set is {$-\frac{2}{7}$}
