Question

solve for x. \\(\frac{2x - 7}{x + 6} = \frac{1}{4}\\) \\(\circ \frac{-7}{34}\\) \\(\circ \frac{34}{7}\\) \\(\circ \frac{-22}{9}\\) \\(\circ \frac{9}{22}\\)

Explanation:

Step1: Cross - multiply to eliminate fractions

Given the equation \(\frac{2x - 7}{x + 6}=\frac{1}{4}\), 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 \(4\times(2x - 7)=1\times(x + 6)\).

Step2: Expand both sides

Expanding the left - hand side: \(4\times2x-4\times7 = 8x-28\).
Expanding the right - hand side: \(x + 6\).
So the equation becomes \(8x-28=x + 6\).

Step3: Isolate the variable \(x\)

Subtract \(x\) from both sides: \(8x-x-28=x - x+ 6\), which simplifies to \(7x-28 = 6\).
Then add 28 to both sides: \(7x-28 + 28=6 + 28\), so \(7x=34\).

Step4: Solve for \(x\)

Divide both sides by 7: \(x=\frac{34}{7}\).

Answer:

\(\frac{34}{7}\)