Question: Solve for x. -6 = -\frac{4}{x-1} Simplify your answer as much as possible. x = [ ]

Solve for x. -6 = -\frac{4}{x-1} Simplify your answer as much as possible. x = [ ]

Solution

To solve for \( x \) in the equation: \[ -6 = \frac{4}{x - 1} \] First, multiply both sides by \( x - 1 \) to eliminate the fraction: \[ -6(x - 1) = 4 \] Distribute \(-6\) on the left side: \[ -6x + 6 = 4 \] Subtract 6 from both sides to isolate \(-6x\): \[ -6x = 4 - 6 \] Simplify the right side: \[ -6x = -2 \] Divide both sides by \(-6\) to solve for \( x \): \[ x = \frac{-2}{-6} \] Simplify the fraction: \[ x = \frac{1}{3} \] Thus, the solution is \( x = \frac{1}{3} \).