e. \( \frac{4 x+5}{2 x+1}=\frac{16}{5} \)

Solve the equation \( \frac{4x+5}{2x+1}=\frac{16}{5} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{4x+5}{2x+1}=\frac{16}{5}\) - step1: Find the domain: \(\frac{4x+5}{2x+1}=\frac{16}{5},x\neq -\frac{1}{2}\) - step2: Cross multiply: \(\left(4x+5\right)\times 5=\left(2x+1\right)\times 16\) - step3: Simplify the equation: \(5\left(4x+5\right)=16\left(2x+1\right)\) - step4: Calculate: \(20x+25=16\left(2x+1\right)\) - step5: Calculate: \(20x+25=32x+16\) - step6: Move the expression to the left side: \(20x+25-\left(32x+16\right)=0\) - step7: Calculate: \(-12x+9=0\) - step8: Move the constant to the right side: \(-12x=0-9\) - step9: Remove 0: \(-12x=-9\) - step10: Change the signs: \(12x=9\) - step11: Divide both sides: \(\frac{12x}{12}=\frac{9}{12}\) - step12: Divide the numbers: \(x=\frac{3}{4}\) - step13: Check if the solution is in the defined range: \(x=\frac{3}{4},x\neq -\frac{1}{2}\) - step14: Find the intersection: \(x=\frac{3}{4}\) The solution to the equation \( \frac{4x+5}{2x+1}=\frac{16}{5} \) is \( x = \frac{3}{4} \) or \( x = 0.75 \).