\begin{tabular}{|l|l|} 1) The quotient of \( x \) and 3 is less than or equal to 5. \\ 2) The difference between \( x \) and 4 is greater than 10. \\ 3) The product of \( x \) and 7 is not greater than 21. \\ 4) \( x \) decreased by 13 is at least 15. \\ 5) \( x \) minus 5 is less than 8. \\ \hline\end{tabular}

To solve the given inequalities, we will translate each statement into an inequality and then solve for \( x \). 1. The quotient of \( x \) and 3 is less than or equal to 5: \[ \frac{x}{3} \leq 5 \] 2. The difference between \( x \) and 4 is greater than 10: \[ x - 4 > 10 \] 3. The product of \( x \) and 7 is not greater than 21: \[ 7x \leq 21 \] 4. \( x \) decreased by 13 is at least 15: \[ x - 13 \geq 15 \] 5. \( x \) minus 5 is less than 8: \[ x - 5 < 8 \] Now, let's solve each inequality step by step. Solve the inequality by following steps: - step0: Solve for \(x\): \(\frac{x}{3}\leq 5\) - step1: Multiply both sides: \(\frac{x}{3}\times 3\leq 5\times 3\) - step2: Multiply the terms: \(x\leq 15\) It seems there was an error in solving the equation \( x - 4 > 10 \). Let's solve it manually. The equation \( x - 4 > 10 \) can be solved by adding 4 to both sides: \[ x > 14 \] Now, let's solve the next inequality. Solve the inequality by following steps: - step0: Solve for \(x\): \(7x\leq 21\) - step1: Divide both sides: \(\frac{7x}{7}\leq \frac{21}{7}\) - step2: Divide the numbers: \(x\leq 3\) Solve the equation \( x - 13 \\geq 15 \). Solve the inequality by following steps: - step0: Solve for \(x\): \(x-13\geq 15\) - step1: Move the constant to the right side: \(x\geq 15+13\) - step2: Add the numbers: \(x\geq 28\) Solve the equation \( x - 5 < 8 \). Solve the inequality by following steps: - step0: Solve for \(x\): \(x-5<8\) - step1: Move the constant to the right side: \(x<8+5\) - step2: Add the numbers: \(x<13\) The solutions to the given inequalities are: 1. \( x \leq 15 \) 2. \( x > 14 \) 3. \( x \leq 3 \) 4. \( x \geq 28 \) 5. \( x < 13 \)