\( 4 x \) Solve for \( x \) \( \frac{1}{2} x+\frac{3}{2}(x+1)-\frac{1}{4}=5 \) \( 4 \times \quad A \quad \frac{5}{2} \) \( 4 x \quad \frac{15}{4} \) \( 4 x \)

To solve the equation \( \frac{1}{2} x + \frac{3}{2}(x+1) - \frac{1}{4} = 5 \), start by simplifying the left side. Distribute \( \frac{3}{2} \) to get \( \frac{3}{2}x + \frac{3}{2} \). This gives \( \frac{1}{2}x + \frac{3}{2}x + \frac{3}{2} - \frac{1}{4} = 5 \). Combining the \( x \) terms results in \( 2x + \frac{3}{2} - \frac{1}{4} = 5 \). Converting \( \frac{3}{2} - \frac{1}{4} \) to a common denominator yields \( \frac{6}{4} - \frac{1}{4} = \frac{5}{4} \). Thus, your equation simplifies to \( 2x + \frac{5}{4} = 5 \). Subtract \( \frac{5}{4} \) from both sides to find \( 2x = 5 - \frac{5}{4} = \frac{20}{4} - \frac{5}{4} = \frac{15}{4} \). Dividing by \( 2 \) gives \( x = \frac{15}{8} \). Now, just multiply that by 4! This gives \( 4x = 4 \times \frac{15}{8} = \frac{60}{8} = \frac{15}{2} \)!