Question

solve for x using cross multiplication.\\(\frac{x - 1}{4} = \frac{2x + 4}{5}\\)\\(x = ?\\)

Explanation:

Step1: Apply cross - multiplication

Cross - multiply the equation \(\frac{x - 1}{4}=\frac{2x + 4}{5}\). According to the cross - multiplication rule \(\frac{a}{b}=\frac{c}{d}\) implies \(a\times d=b\times c\). So we get \(5(x - 1)=4(2x + 4)\).

Step2: Expand both sides

Expand the left - hand side: \(5(x - 1)=5x-5\). Expand the right - hand side: \(4(2x + 4)=8x + 16\). Now the equation becomes \(5x-5 = 8x+16\).

Step3: Move the terms with x to one side and constants to the other

Subtract \(5x\) from both sides: \(5x-5x - 5=8x-5x + 16\), which simplifies to \(-5 = 3x+16\). Then subtract 16 from both sides: \(-5-16=3x+16 - 16\), so \(-21 = 3x\).

Step4: Solve for x

Divide both sides by 3: \(x=\frac{-21}{3}=-7\).

Answer:

\(x=-7\)