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

iohanetc 2021-09-24 Answered
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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Expert Answer

Nicole Conner
Answered 2021-09-25 Author has 29430 answers
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
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