Question: (\frac{x + 7}{4} = \frac{x}{3} + 2\)…

\(\frac{x + 7}{4} = \frac{x}{3} + 2\)

Solution

To solve the equation \[ \frac{x + 7}{4} = \frac{x}{3} + 2 \] First, eliminate the fractions by finding a common denominator. The common denominator of 4 and 3 is 12. Multiply every term by 12: \[ 12 \cdot \frac{x + 7}{4} = 12 \cdot \frac{x}{3} + 12 \cdot 2 \] Simplify each term: \[ 3(x + 7) = 4x + 24 \] Distribute the 3 on the left side: \[ 3x + 21 = 4x + 24 \] Subtract \(3x\) from both sides: \[ 21 = x + 24 \] Subtract 24 from both sides to solve for \(x\): \[ 21 - 24 = x \] \[ x = -3 \] The solution is \(x = -3\).