Question

$$\frac{ 3x-1 }{ 6 } - \frac{ x-1 }{ 12 } = \frac{ x-5 }{ 4 } + \frac{ x }{ 6 }$$

Answer

[No Solution]

Solution


Multiply both sides by \(12\) (the LCM of \(6, 12, 4\)).
\[2(3x-1)+1-x=3(x-5)+2x\]
Expand.
\[6x-2+1-x=3x-15+2x\]
Simplify  \(6x-2+1-x\)  to  \(5x-1\).
\[5x-1=3x-15+2x\]
Simplify  \(3x-15+2x\)  to  \(5x-15\).
\[5x-1=5x-15\]
Cancel \(5x\) on both sides.
\[-1=-15\]
Since \(-1=-15\) is false, there is no solution.
No Solution