Solve the equation: (y+5)/3 − (y−3)/2 = 5

Question

ScanSolve AI Tutor · Accepted Answer

Your solution is correct! Here are the steps to find $y$ :

Start with the given equation.
$\frac{y+5}{3} - \frac{y-3}{2} = 5$
Find a common denominator for the fractions, which is 6.
Rewrite the fractions with the common denominator.
$\frac{2(y+5)}{6} - \frac{3(y-3)}{6} = 5$ $\frac{2(y+5) - 3(y-3)}{6} = 5$
Distribute the numbers into the parentheses in the numerator.
Be careful with the negative sign.
$\frac{2y+10 - 3y+9}{6} = 5$
Combine like terms in the numerator ( $2y - 3y$ and $10 + 9$ ).
$\frac{-y+19}{6} = 5$
Multiply both sides of the equation by 6 to eliminate the denominator.
$-y+19 = 5 \times 6$ $-y+19 = 30$
Subtract 19 from both sides of the equation.
$-y = 30 - 19$ $-y = 11$
Multiply both sides by -1 to solve for $y$ .
$y = -11$

Solve the equation: (y+5)/3 - (y-3)/2 = 5