Solve the inequality. Write the inequality in interval notation, and graph it. \( 8(t-3)>5(t-7) \) The solution set is (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Solve the equation \( 8(t-3)>5(t-7) \). Solve the inequality by following steps: - step0: Solve for \(t\): \(8\left(t-3\right)>5\left(t-7\right)\) - step1: Calculate: \(8t-24=5\left(t-7\right)\) - step2: Calculate: \(8t-24=5t-35\) - step3: Move the expression to the left side: \(8t-24-\left(5t-35\right)>0\) - step4: Calculate: \(3t+11>0\) - step5: Move the constant to the right side: \(3t>0-11\) - step6: Remove 0: \(3t>-11\) - step7: Divide both sides: \(\frac{3t}{3}>\frac{-11}{3}\) - step8: Divide the numbers: \(t>-\frac{11}{3}\) The solution to the inequality \(8(t-3)>5(t-7)\) is \(t > -\frac{11}{3}\). To write this in interval notation, we can express it as \((-\frac{11}{3}, \infty)\). To graph this inequality, we can plot the point \(-\frac{11}{3}\) on the number line and shade the region to the right of this point, indicating that all values greater than \(-\frac{11}{3}\) are part of the solution set.