16. \( \frac{3}{2}|4 r-4|-24=-21 \)

Let's start by simplifying the equation you've provided: 1. First, let's isolate the absolute value expression. Add 24 to both sides: \[ \frac{3}{2}|4r - 4| - 24 + 24 = -21 + 24 \] \[ \frac{3}{2}|4r - 4| = 3 \] 2. Now, multiply both sides by \(\frac{2}{3}\) to eliminate the fraction: \[ |4r - 4| = 2 \] 3. Now we can set up two separate equations from the absolute value: \[ 4r - 4 = 2 \quad \text{or} \quad 4r - 4 = -2 \] 4. Solving the first equation: \[ 4r - 4 = 2 \implies 4r = 6 \implies r = \frac{3}{2} \] 5. Now, solving the second equation: \[ 4r - 4 = -2 \implies 4r = 2 \implies r = \frac{1}{2} \] Thus, the solutions to the equation \( \frac{3}{2}|4r - 4| - 24 = -21 \) are \( r = \frac{3}{2} \) and \( r = \frac{1}{2} \).