Question

solve for x.
\\(\frac{7}{x} = \frac{15}{x} + 14\\)
simplify your answer as much as possible.

Explanation:

Step1: Subtract \(\frac{15}{x}\) from both sides

\(\frac{7}{x}-\frac{15}{x}=\frac{15}{x}+14-\frac{15}{x}\)
Simplify left side: \(\frac{7 - 15}{x}=\frac{-8}{x}\)
Right side: \(14\)
So we get \(\frac{-8}{x}=14\)

Step2: Cross - multiply to solve for \(x\)

From \(\frac{-8}{x}=14\), we can rewrite it as \(14x=-8\)

Step3: Divide both sides by 14

\(x = \frac{-8}{14}\)
Simplify the fraction: \(x=-\frac{4}{7}\)

Answer:

\(x = -\frac{4}{7}\)