Answer
y = -6
Work Step by Step
We start with the original equation:
$\frac{y}{3}$ + $\frac{2}{5}$ = $\frac{y}{5}$ - $\frac{2}{5}$
We can start by finding the least common denominator for all of the fractions. The least common denominator is 15. We can now write all of the fractions as equivalents with a denominator of 15.
This gives us: $\frac{5y}{15}$ + $\frac{6}{15}$ = $\frac{3y}{15}$ - $\frac{6}{15}$
We can now subtract $\frac{3y}{15}$ from both sides of the equation.
$\frac{5y}{15}$ - $\frac{3y}{15}$ + $\frac{6}{15}$ = $\frac{3y}{15}$ - $\frac{3y}{15}$ - $\frac{6}{15}$
Completing the arithmetic, we get:
$\frac{2y}{15}$ + $\frac{6}{15}$ = -$\frac{6}{15}$
Next, subtract $\frac{6}{15}$ from both sides of the equation.
$\frac{2y}{15}$ + $\frac{6}{15}$ - $\frac{6}{15}$ = -$\frac{6}{15}$ - $\frac{6}{15}$
Complete the arithmetic: $\frac{2y}{15}$ = $\frac{-12}{15}$
Now, cross multiply so that: 2y(15) = (-12)(15)
And, 30y = -180
Last, divide both sides by 30.
$\frac{30y}{30}$ = $\frac{-180}{30}$
Complete the division and get y = -6.
We can check by substituting -6 back into the original equations for y.
$\frac{-6}{3}$ + $\frac{2}{5}$ = $\frac{-6}{5}$ - $\frac{2}{5}$
Now, complete the arithmetic on each side of the equation.
-2 + $\frac{2}{5}$ = $\frac{-8}{5}$
$\frac{-10}{5}$ + $\frac{2}{5}$ = $\frac{-8}{5}$
In the step above, we rewrote -2 as a fraction using a denominator of 5.
We get $\frac{-8}{5}$ = $\frac{-8}{5}$
Showing that our solution of y = -6 is correct.
