Question

solve for x.
\\( -dfrac{5}{x - 7} = 2 \\)
simplify your answer as much as possible.
\\( x = \\)
no solution \\( sqrt{square} \\) \\( dfrac{square}{square} \\) \\( square.square... \\)

Explanation:

Step1: Multiply both sides by \(x - 7\)

To eliminate the denominator, we multiply both sides of the equation \(-\frac{5}{x - 7}=2\) by \(x - 7\) (assuming \(x
eq7\) to avoid division by zero). This gives us \(-5 = 2(x - 7)\).

Step2: Distribute the 2

Using the distributive property \(a(b - c)=ab - ac\), we expand the right - hand side: \(-5=2x-14\).

Step3: Add 14 to both sides

To isolate the term with \(x\), we add 14 to both sides of the equation. So, \(-5 + 14=2x-14 + 14\), which simplifies to \(9 = 2x\).

Step4: Divide by 2

To solve for \(x\), we divide both sides of the equation \(9 = 2x\) by 2. We get \(x=\frac{9}{2}\) or \(x = 4.5\). We also need to check if this solution makes the original denominator non - zero. When \(x=\frac{9}{2}\), \(x - 7=\frac{9}{2}-7=\frac{9 - 14}{2}=-\frac{5}{2}
eq0\), so the solution is valid.

Answer:

\(x=\frac{9}{2}\)