Question: b) \(\frac{1}{2} - \frac{x}{4} = \frac{1}{5}\)

Solution

To solve the equation \[ \frac{1}{2} - \frac{x}{4} = \frac{1}{5} \] we first want to eliminate the fractions by finding a common denominator. The common denominator for 2, 4, and 5 is 20. We will multiply every term by 20. Multiply through by 20: \[ 20 \cdot \frac{1}{2} - 20 \cdot \frac{x}{4} = 20 \cdot \frac{1}{5} \] Simplify each term: \[ 10 - 5x = 4 \] Next, solve for \(x\) by isolating it on one side. Subtract 10 from both sides: \[ -5x = 4 - 10 \] Simplify: \[ -5x = -6 \] Divide each side by -5: \[ x = \frac{-6}{-5} \] Simplify further: \[ x = \frac{6}{5} \] The solution is \(x = \frac{6}{5}\).