# Determine whether the given problem is an equation or an expression. If it is an

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. y/3 + (y - 5)/10 = (4y + 3)/5

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Step 1
Given:
$$\displaystyle{\frac{{{y}}}{{{3}}}}+{\frac{{{y}-{5}}}{{{10}}}}={\frac{{{4}{y}+{3}}}{{{5}}}}$$
It contains an equal sign therefore it is an equation.
$$\displaystyle{\frac{{{y}}}{{{3}}}}+{\frac{{{y}-{5}}}{{{10}}}}={\frac{{{4}{y}+{3}}}{{{5}}}}$$
$$\displaystyle\Rightarrow{\frac{{{10}{y}+{3}{\left({y}-{5}\right)}}}{{{30}}}}={\frac{{{4}{y}+{3}}}{{{5}}}}$$
$$\displaystyle\Rightarrow{\frac{{{10}{y}+{3}{y}-{15}}}{{{30}}}}={\frac{{{4}{y}_{{3}}}}{{{5}}}}$$
$$\displaystyle\Rightarrow{\frac{{{13}{y}-{15}}}{{{30}}}}={\frac{{{4}{y}+{3}}}{{{5}}}}$$
$$\displaystyle\Rightarrow{\frac{{{13}{y}-{15}}}{{{30}}}}={\frac{{{6}{\left({4}{y}+{3}\right)}}}{{{30}}}}$$
$$\displaystyle\Rightarrow{13}{y}-{15}={24}{y}+{18}$$
$$\displaystyle\Rightarrow-{33}={11}{y}$$
$$\displaystyle\Rightarrow{y}=-{3}$$
Step 2
Therefore,
y=-3