Question: Solve for x. 2 = \frac{3}{7} - \frac{6}{x} Simplify your answer as much as possible. x = [ ]

Solve for x. 2 = \frac{3}{7} - \frac{6}{x} Simplify your answer as much as possible. x = [ ]

Solution

To solve the equation \[ 2 - \frac{3}{7} = \frac{6}{x} \] First, isolate \(\frac{6}{x}\) by moving \(\frac{3}{7}\) to the other side: \[ 2 - \frac{3}{7} = \frac{6}{x} \] Convert 2 into a fraction with a denominator of 7: \[ \frac{14}{7} - \frac{3}{7} = \frac{6}{x} \] Subtract the fractions on the left side: \[ \frac{11}{7} = \frac{6}{x} \] Cross-multiply to solve for \(x\): \[ 11x = 42 \] Divide both sides by 11: \[ x = \frac{42}{11} \] So the solution is: \[ x = \frac{42}{11} \]