10.\(3m=5m-\frac { 8 }{ 5 } \)

Given that, \(3m=5m-\frac { 8 }{ 5 } \)
\(\Rightarrow 3m-5m=-\frac {8 }{ 5 } \quad \)[Transposing 5m to LHS]

\(\Rightarrow -2m=-\frac {8 }{ 5 } \)

\(\Rightarrow \frac{-2m}{-2}=\frac{-\frac {8 }{ 5 }}{-2}\quad \)[Dividing both the sides by -2]

\(\Rightarrow m=\frac {4}{ 5 }\)

Thus,\( m=\frac {4}{ 5 }\) is the required solution

Checking:

Substituting \(m=\frac {4}{ 5 }\) in the given equation, we have

LHS=\(3×\frac{4}5 =\frac{12}5\)

RHS=\(4×\frac{4}5 - \frac{8}5=\frac{20}5-\frac{8}5 =\frac{12}5\)

RHS=LHS

Hence,\( m=\frac {4}{ 5 }\) is the required solution