(23) \( \frac{1}{3}(2 x-1)=\frac{3}{4}(x+2) \)

To solve the equation: \[ \frac{1}{3}(2x - 1) = \frac{3}{4}(x + 2) \] **Step 1: Eliminate the Fractions** Find the least common multiple (LCM) of the denominators 3 and 4, which is 12. Multiply both sides of the equation by 12 to eliminate the fractions: \[ 12 \cdot \frac{1}{3}(2x - 1) = 12 \cdot \frac{3}{4}(x + 2) \] Simplify each side: \[ 4(2x - 1) = 9(x + 2) \] **Step 2: Distribute the Multiplications** Expand both sides of the equation: \[ 8x - 4 = 9x + 18 \] **Step 3: Solve for \( x \)** First, subtract \( 8x \) from both sides to get all \( x \)-terms on one side: \[ -4 = x + 18 \] Next, subtract 18 from both sides to isolate \( x \): \[ -4 - 18 = x \] \[ -22 = x \] **Solution:** \[ x = -22 \]