Question

solve for x.
-3 = \frac{8}{x - 5}
simplify your answer as much as possible.

Explanation:

Step1: Cross - multiply to eliminate the fraction

To solve the equation \(-3=\frac{8}{x - 5}\), we can cross - multiply. Multiply both sides of the equation by \(x-5\) (assuming \(x
eq5\) to avoid division by zero). We get \(-3(x - 5)=8\).

Step2: Distribute the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), where \(a=-3\), \(b = x\) and \(c=-5\), we have \(-3x+15 = 8\).

Step3: Isolate the variable term

Subtract 15 from both sides of the equation: \(-3x=8 - 15\). Simplifying the right - hand side, we get \(-3x=-7\).

Step4: Solve for x

Divide both sides of the equation by \(-3\): \(x=\frac{-7}{-3}=\frac{7}{3}\).

Answer:

\(\frac{7}{3}\) (or \(2\frac{1}{3}\))