Answer
{$\frac{5}{12}$}
Work Step by Step
Step 1: $\frac{7}{4}+\frac{1}{5}x-\frac{3}{2}=\frac{4}{5}x$
Step 2: Multiplying both sides by 20, the LCD of the fractions:
$20(\frac{7}{4}+\frac{1}{5}x-\frac{3}{2})=20(\frac{4}{5}x)$
Step 3: $20(\frac{7}{4})+20(\frac{1}{5}x)-20(\frac{3}{2})=20(\frac{4}{5}x)$
Step 4: $35+4x-30=16x$
Step 5: $4x+5=16x$
Step 6: Subtracting $16x$ from both sides, $4x+5-16x=16x-16x$
Step 7: $-12x+5=0$
Step 8: Subtracting $5$ from both sides, $-12x+5-5=0-5$
Step 9: $-12x=-5$
Step 10: Dividing both sides by $-12$,
$\frac{-12x}{-12}=\frac{-5}{-12}$
Step 11: $x=\frac{5}{12}$
Check:
Step 1: Substituting the answer in the initial equation,
$\frac{7}{4}+\frac{1}{5}(\frac{5}{12})-\frac{3}{2}=\frac{4}{5}(\frac{5}{12})$
Step 2: $\frac{7}{4}+(\frac{1}{12})-\frac{3}{2}=(\frac{4}{12})$
Step 3: $\frac{7(3)+1-6(3)}{12}=\frac{1}{3}$
Step 4: $\frac{21+1-18}{12}=\frac{1}{3}$
Step 5: $\frac{22-18}{12}=\frac{1}{3}$
Step 6: $\frac{4}{12}=\frac{1}{3}$
Step 7: $\frac{1}{3}=\frac{1}{3}$
Since the solution checks, the solution set is {$\frac{5}{12}$}
