Question

1. \\(\frac{x + 2}{3} = \frac{x + 4}{5}\\)

Explanation:

Step1: Cross - multiply to eliminate denominators

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

Step2: Expand both sides

Expanding the left - hand side: \(5(x + 2)=5x+10\).
Expanding the right - hand side: \(3(x + 4)=3x + 12\).
So the equation becomes \(5x+10 = 3x+12\).

Step3: Isolate the variable \(x\)

Subtract \(3x\) from both sides: \(5x-3x + 10=3x-3x + 12\), which simplifies to \(2x+10 = 12\).
Then subtract 10 from both sides: \(2x+10 - 10=12 - 10\), so \(2x=2\).

Step4: Solve for \(x\)

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

Answer:

\(x = 1\)