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Dwight Williams

Solve  \frac{m - 4}{ 4}=\frac{m - 5}{5}

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Answer:

The value of m is 0.

Step-by-step-explanation:

We have given that,

\displaystyle{\sf\:\dfrac{m\:-\:4}{4}\:=\:\dfrac{m\:-\:5}{5}}

We have to find the value of m.

Now,

\displaystyle{\sf\:\dfrac{m\:-\:4}{4}\:=\:\dfrac{m\:-\:5}{5}}

\displaystyle{\implies\sf\:5\:\times\:(\:m\:-\:4\:)\:=\:4\:\times\:(\:m\:-\:5\:)}

\displaystyle{\implies\sf\:5m\:-\:20\:=\:4m\:-\:20}

\displaystyle{\implies\sf\:5m\:-\:4m\:=\:-\:20\:+\:20}

\displaystyle{\implies\boxed{\red{\sf\:m\:=\:0}}}

The value of m is 0.

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Verification:

The given equation is

\displaystyle{\sf\:\dfrac{m\:-\:4}{4}\:=\:\dfrac{m\:-\:5}{5}}

We have, m = 0.

By substituting m = 0 in the LHS of the given equation, we get,

\displaystyle{\sf\:LHS\:=\:\dfrac{m\:-\:4}{4}}

\displaystyle{\implies\sf\:LHS\:=\:\dfrac{0\:-\:4}{4}}

\displaystyle{\implies\sf\:LHS\:=\:-\:\cancel{\dfrac{4}{4}}}

\displaystyle{\implies\boxed{\red{\sf\:LHS\:=\:-\:1}}}

Now, by substituting m = 0 in the RHS of the given equation, we get,

\displaystyle{\sf\:RHS\:=\:\dfrac{m\:-\:5}{5}}

\displaystyle{\implies\sf\:RHS\:=\:\dfrac{0\:-\:5}{5}}

\displaystyle{\implies\sf\:RHS\:=\:-\:\cancel{\dfrac{5}{5}}}

\displaystyle{\implies\boxed{\red{\sf\:RHS\:=\:-\:1}}}

\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:LHS\:=\:RHS}}}}

Hence verified!

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