Question

solve for x and simplify the answer fully.\\(\frac{x - 4}{x - 2} = \frac{7}{9}\\)\
answer attempt 1 out of 2\
\\(x = \\) input box submit answer

Explanation:

Step1: Cross - multiply the equation

To solve the equation \(\frac{x - 4}{x - 2}=\frac{7}{9}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\) (where \(b
eq0\) and \(d
eq0\)), then \(a\times d=b\times c\). So we get \(9(x - 4)=7(x - 2)\).

Step2: Expand both sides

Expand the left - hand side: \(9\times x-9\times4 = 9x-36\). Expand the right - hand side: \(7\times x-7\times2=7x - 14\). Now our equation is \(9x-36 = 7x-14\).

Step3: Isolate the variable \(x\)

Subtract \(7x\) from both sides of the equation: \(9x-7x-36=7x - 7x-14\), which simplifies to \(2x-36=-14\). Then add 36 to both sides: \(2x-36 + 36=-14 + 36\), so \(2x=22\).

Step4: Solve for \(x\)

Divide both sides of the equation \(2x = 22\) by 2: \(\frac{2x}{2}=\frac{22}{2}\), which gives \(x = 11\). We also need to check if this solution makes the original denominator non - zero. For the original equation \(\frac{x - 4}{x - 2}=\frac{7}{9}\), when \(x = 11\), the denominator \(x-2=11 - 2=9
eq0\), so \(x = 11\) is a valid solution.

Answer:

\(x = 11\)