Question

solve for x and simplify the answer fully.
\\(\frac{2x + 7}{7} = \frac{x - 7}{4}\\)

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{2x + 7}{7}=\frac{x - 7}{4}\), we use the cross - multiplication property. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\). So we have \((2x + 7)\times4=7\times(x - 7)\).

Step2: Expand both sides

Expand the left - hand side: \(4\times(2x)+4\times7 = 8x+28\).
Expand the right - hand side: \(7\times x-7\times7=7x - 49\).
Now our equation becomes \(8x + 28=7x-49\).

Step3: Isolate the variable x

Subtract \(7x\) from both sides of the equation: \(8x-7x + 28=7x-7x-49\), which simplifies to \(x + 28=-49\).
Then subtract 28 from both sides: \(x+28 - 28=-49 - 28\).

Answer:

\(x=-77\)