Question

solve for x using cross multiplication.
\\(\frac{4x + 6}{3} = \frac{x + 9}{2}\\)
\\(x = ?\\)

Explanation:

Step1: Apply cross - multiplication

For the equation \(\frac{4x + 6}{3}=\frac{x + 9}{2}\), cross - multiplying gives \(2(4x + 6)=3(x + 9)\).

Step2: Expand both sides

Expanding the left - hand side: \(2\times4x+2\times6 = 8x + 12\).
Expanding the right - hand side: \(3\times x+3\times9=3x + 27\). So the equation becomes \(8x + 12 = 3x+27\).

Step3: Subtract \(3x\) from both sides

\(8x-3x + 12=3x - 3x+27\), which simplifies to \(5x+12 = 27\).

Step4: Subtract 12 from both sides

\(5x+12 - 12=27 - 12\), so \(5x=15\).

Step5: Divide both sides by 5

\(\frac{5x}{5}=\frac{15}{5}\), which gives \(x = 3\).

Answer:

\(x = 3\)