Question

$$m-\frac{m-1}{2}=\underline{1}-\frac{m-2}{3}$$

Answer

m=7/5

Solution


Multiply both sides by \(6\) (the LCM of \(2, 3\)).
\[6m-3(m-1)=6-2(m-2)\]
Expand.
\[6m-3m+3=6-2m+4\]
Simplify  \(6m-3m+3\)  to  \(3m+3\).
\[3m+3=6-2m+4\]
Simplify  \(6-2m+4\)  to  \(-2m+10\).
\[3m+3=-2m+10\]
Subtract \(3\) from both sides.
\[3m=-2m+10-3\]
Simplify  \(-2m+10-3\)  to  \(-2m+7\).
\[3m=-2m+7\]
Add \(2m\) to both sides.
\[3m+2m=7\]
Simplify  \(3m+2m\)  to  \(5m\).
\[5m=7\]
Divide both sides by \(5\).
\[m=\frac{7}{5}\]

Decimal Form: 1.4