Algebra 3 Test \( \frac{1}{4 x}-\frac{3}{4}=\frac{7}{x} \)

Solve the equation \( \frac{1}{4x}-\frac{3}{4}=\frac{7}{x} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{1}{4x}-\frac{3}{4}=\frac{7}{x}\) - step1: Find the domain: \(\frac{1}{4x}-\frac{3}{4}=\frac{7}{x},x\neq 0\) - step2: Multiply both sides of the equation by LCD: \(\left(\frac{1}{4x}-\frac{3}{4}\right)\times 4x=\frac{7}{x}\times 4x\) - step3: Simplify the equation: \(1-3x=28\) - step4: Move the constant to the right side: \(-3x=28-1\) - step5: Subtract the numbers: \(-3x=27\) - step6: Change the signs: \(3x=-27\) - step7: Divide both sides: \(\frac{3x}{3}=\frac{-27}{3}\) - step8: Divide the numbers: \(x=-9\) - step9: Check if the solution is in the defined range: \(x=-9,x\neq 0\) - step10: Find the intersection: \(x=-9\) The solution to the equation \( \frac{1}{4x}-\frac{3}{4}=\frac{7}{x} \) is \( x=-9 \).