Question

1. \\(\frac{x + 2}{6} = \frac{2x - 10}{8}\\)

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{x + 2}{6}=\frac{2x-10}{8}\), we cross - multiply. That is, we multiply the numerator of the left - hand side by the denominator of the right - hand side and set it equal to the numerator of the right - hand side multiplied by the denominator of the left - hand side. So we get \(8(x + 2)=6(2x - 10)\).

Step2: Expand both sides

Using the distributive property \(a(b + c)=ab+ac\), we expand the left - hand side: \(8x+16\) and the right - hand side: \(12x-60\). So the equation becomes \(8x + 16=12x-60\).

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

Subtract \(8x\) from both sides: \(8x - 8x+16=12x-8x - 60\), which simplifies to \(16 = 4x-60\). Then add 60 to both sides: \(16 + 60=4x-60 + 60\), so \(76 = 4x\).

Step4: Solve for x

Divide both sides by 4: \(\frac{76}{4}=\frac{4x}{4}\), which gives \(x = 19\).

Answer:

\(x = 19\)