Solve the equation \( \frac{3-x}{5} + \frac{x-2}{4} = -2 \)

Answer

To solve the equation \( \frac{3-x}{5} + \frac{x-2}{4} = -2 \), we first eliminate the fractions. We can do this by finding a common denominator. The denominators are 5 and 4, and their least common multiple is 20. 1. Multiply every term in the equation by 20 to eliminate the fractions: \[ 20 \left( \frac{3-x}{5} \right) + 20 \left( \frac{x-2}{4} \right) = 20 \cdot (-2) \] This simplifies to: \[ 4(3-x) + 5(x-2) = -40 \] 2. Distribute the terms: \[ 12 - 4x + 5x - 10 = -40 \] 3. Combine like terms: \[ 12 - 10 + x = -40 \] This simplifies to: \[ 2 + x = -40 \] 4. Isolate the variable \( x \): \[ x = -40 - 2 \] \[ x = -42 \] Thus, the solution to the equation is \( x = -42 \).