b. \( \frac{12}{t}+\frac{3}{2}=4 \)

To solve the equation \( \frac{12}{t} + \frac{3}{2} = 4 \), first, we can isolate the term with \( t \). Subtract \( \frac{3}{2} \) from both sides: \[ \frac{12}{t} = 4 - \frac{3}{2} \] Now, convert \( 4 \) into a fraction with a denominator of \( 2 \): \[ 4 = \frac{8}{2} \] So, we have: \[ \frac{12}{t} = \frac{8}{2} - \frac{3}{2} = \frac{5}{2} \] Next, we cross-multiply to eliminate the fraction: \[ 12 \cdot 2 = 5t \] Simplifying gives: \[ 24 = 5t \] Now, divide both sides by \( 5 \): \[ t = \frac{24}{5} = 4.8 \] Therefore, the solution to the equation is \( t = 4.8 \). To check our work, substitute \( t = 4.8 \) back into the original equation: \[ \frac{12}{4.8} + \frac{3}{2} = 4 \] Calculating \( \frac{12}{4.8} \) gives \( 2.5 \), and adding \( 1.5 \) (which is \( \frac{3}{2} \)) results in \( 4 \), confirming our solution is correct!