Question

solve for x.
\\(\frac{x - 2}{6} = \frac{2}{9}\\)
simplify your answer as much as possible.
\\(x = \square\\)

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{x - 2}{6}=\frac{2}{9}\), we can use the cross - multiplication property. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\). So, we have \((x - 2)\times9=6\times2\).

Step2: Simplify both sides of the equation

First, simplify the right - hand side: \(6\times2 = 12\). The left - hand side becomes \(9(x - 2)=9x-18\). So our equation is \(9x-18 = 12\).

Step3: Solve for x

Add 18 to both sides of the equation: \(9x-18 + 18=12 + 18\). This simplifies to \(9x=30\). Then divide both sides by 9: \(x=\frac{30}{9}\). Simplify the fraction \(\frac{30}{9}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So \(x=\frac{10}{3}\).

Answer:

\(\frac{10}{3}\)