Question

$$3-5 \frac{ y }{ 4 } =2-4 \frac{ y }{ 3 }$$

Answer

y=-12

Solution


Simplify  \(5\times \frac{y}{4}\)  to  \(\frac{5y}{4}\).
\[3-\frac{5y}{4}=2-4\times \frac{y}{3}\]
Simplify  \(4\times \frac{y}{3}\)  to  \(\frac{4y}{3}\).
\[3-\frac{5y}{4}=2-\frac{4y}{3}\]
Multiply both sides by \(12\) (the LCM of \(4, 3\)).
\[36-15y=24-16y\]
Subtract \(24\) from both sides.
\[36-15y-24=-16y\]
Simplify  \(36-15y-24\)  to  \(-15y+12\).
\[-15y+12=-16y\]
Add \(15y\) to both sides.
\[12=-16y+15y\]
Simplify  \(-16y+15y\)  to  \(-y\).
\[12=-y\]
Multiply both sides by \(-1\).
\[-12=y\]
Switch sides.
\[y=-12\]