Question

1. solve: \\(\frac{x - 9}{6} = \frac{x + 7}{3}\\)

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{x - 9}{6}=\frac{x + 7}{3}\), cross - multiplying (which is based on the property that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)) gives us \(3(x - 9)=6(x + 7)\).

Step2: Expand both sides

Expand the left - hand side: \(3x-27\), and expand the right - hand side: \(6x + 42\). So the equation becomes \(3x-27 = 6x+42\).

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

Subtract \(3x\) from both sides: \(3x-3x - 27=6x-3x + 42\), which simplifies to \(-27 = 3x+42\). Then subtract 42 from both sides: \(-27-42=3x+42 - 42\), so \(-69 = 3x\).

Step4: Solve for x

Divide both sides by 3: \(x=\frac{-69}{3}=-23\).

Answer:

\(x = - 23\)