Question

$$\frac{ 1 }{ 4 } (x-1)- \frac{ 1 }{ 5 } (x-3)=0.6$$

Answer

x=5

Solution


Simplify  \(\frac{1}{4}(x-1)\)  to  \(\frac{x-1}{4}\).
\[\frac{x-1}{4}-\frac{1}{5}(x-3)=0.6\]
Simplify  \(\frac{1}{5}(x-3)\)  to  \(\frac{x-3}{5}\).
\[\frac{x-1}{4}-\frac{x-3}{5}=0.6\]
Multiply both sides by \(20\) (the LCM of \(4, 5\)).
\[5(x-1)-4(x-3)=12\]
Expand.
\[5x-5-4x+12=12\]
Simplify  \(5x-5-4x+12\)  to  \(x+7\).
\[x+7=12\]
Subtract \(7\) from both sides.
\[x=12-7\]
Simplify  \(12-7\)  to  \(5\).
\[x=5\]