Answer
{$10$}
Work Step by Step
Step 1: $\frac{1}{14}(3x-2)=\frac{x+10}{10}$
Step 2: $\frac{3x-2}{14}= \frac{x+10}{10}$
Step 3: Through cross multiplication, $10(3x-2)=14(x+10)$
Step 4: $30x-20=14x+140$
Step 5: Subtracting $14x$ from both sides, $30x-20-14x=14x-14x+140$
Step 6: $16x-20=140$
Step 7: Adding $20$ to both sides, $16x-20+20=140+20$
Step 8: $16x=160$
Step 9: Dividing both sides by $16$,
$\frac{16x}{16}=\frac{160}{16}$
Step 10: $x=10$
Check:
Step 1: Substituting the answer in the initial equation,
$\frac{1}{14}(3(10)-2)=\frac{10+10}{10}$
Step 2: $\frac{1}{14}(30-2)=\frac{20}{10}$
Step 3: $\frac{1}{14}(28)=2$
Step 4: $2=2$
Step 5 $0=0$
Since the solution checks, the solution set is {$10$}.
