Question

$\frac{3x - 1}{2}=\frac{5x - 3}{4}$

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{3x - 1}{2}=\frac{5x - 3}{4}\), we cross - multiply. Cross - multiplying gives us \(4\times(3x - 1)=2\times(5x - 3)\).

Step2: Expand both sides

Expand the left - hand side: \(4\times(3x - 1)=12x-4\). Expand the right - hand side: \(2\times(5x - 3)=10x - 6\). So the equation becomes \(12x-4 = 10x-6\).

Step3: Move like terms to the same side

Subtract \(10x\) from both sides: \(12x-10x - 4=10x-10x - 6\), which simplifies to \(2x-4=-6\). Then add 4 to both sides: \(2x-4 + 4=-6 + 4\), so \(2x=-2\).

Step4: Solve for x

Divide both sides by 2: \(\frac{2x}{2}=\frac{-2}{2}\), which gives \(x=-1\).

Answer:

\(x = - 1\)