Solve the equation and check \( \frac{9 t}{14}-\frac{t}{2}=1 \)

To solve the equation \( \frac{9 t}{14} - \frac{t}{2} = 1 \), we first find a common denominator for the fractions. The least common multiple of 14 and 2 is 14. Rewriting the equation with a common denominator: \[ \frac{9t}{14} - \frac{7t}{14} = 1 \] Now, combine the fractions: \[ \frac{9t - 7t}{14} = 1 \] This simplifies to: \[ \frac{2t}{14} = 1 \] Next, we simplify the fraction: \[ \frac{t}{7} = 1 \] Multiplying both sides by 7 gives: \[ t = 7 \] Now, let's check the solution by substituting \( t = 7 \) back into the original equation: \[ \frac{9(7)}{14} - \frac{7}{2} = 1 \] This simplifies to: \[ \frac{63}{14} - \frac{7}{2} \] Calculating \( \frac{63}{14} = 4.5 \) and \( \frac{7}{2} = 3.5 \): Now: \[ 4.5 - 3.5 = 1 \] Since both sides of the equation equal 1, the solution \( t = 7 \) is verified!