Question

$$y+6/4+y+3/5=5y-4/8$$

Answer

y=13/15

Solution


Simplify  \(\frac{6}{4}\)  to  \(\frac{3}{2}\).
\[y+\frac{3}{2}+y+\frac{3}{5}=5y-\frac{4}{8}\]
Simplify  \(\frac{4}{8}\)  to  \(\frac{1}{2}\).
\[y+\frac{3}{2}+y+\frac{3}{5}=5y-\frac{1}{2}\]
Simplify  \(y+\frac{3}{2}+y+\frac{3}{5}\)  to  \(2y+\frac{21}{10}\).
\[2y+\frac{21}{10}=5y-\frac{1}{2}\]
Subtract \(2y\) from both sides.
\[\frac{21}{10}=5y-\frac{1}{2}-2y\]
Simplify  \(5y-\frac{1}{2}-2y\)  to  \(3y-\frac{1}{2}\).
\[\frac{21}{10}=3y-\frac{1}{2}\]
Add \(\frac{1}{2}\) to both sides.
\[\frac{21}{10}+\frac{1}{2}=3y\]
Simplify  \(\frac{21}{10}+\frac{1}{2}\)  to  \(\frac{13}{5}\).
\[\frac{13}{5}=3y\]
Divide both sides by \(3\).
\[\frac{\frac{13}{5}}{3}=y\]
Simplify  \(\frac{\frac{13}{5}}{3}\)  to  \(\frac{13}{5\times 3}\).
\[\frac{13}{5\times 3}=y\]
Simplify  \(5\times 3\)  to  \(15\).
\[\frac{13}{15}=y\]
Switch sides.
\[y=\frac{13}{15}\]

Decimal Form: 0.866667