3х:11=1 1/2 : 2 3/4

To solve the equation \( \frac{3x}{11} = \frac{1 \frac{1}{2}}{2 \frac{3}{4}} \), we first need to convert the mixed numbers into improper fractions. 1. Convert \( 1 \frac{1}{2} \): \[ 1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2} \] 2. Convert \( 2 \frac{3}{4} \): \[ 2 \frac{3}{4} = \frac{4 \times 2 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \] Now we rewrite the equation: \[ \frac{3x}{11} = \frac{\frac{3}{2}}{\frac{11}{4}} \] To simplify the right side, we multiply by the reciprocal: \[ \frac{3}{2} \div \frac{11}{4} = \frac{3}{2} \times \frac{4}{11} = \frac{12}{22} = \frac{6}{11} \] Now the equation becomes: \[ \frac{3x}{11} = \frac{6}{11} \] To eliminate the denominators, multiply both sides by 11: \[ 3x = 6 \] Next, divide both sides by 3 to solve for \( x \): \[ x = \frac{6}{3} = 2 \] Thus, the solution is: \[ \boxed{2} \]