8) \( \frac{1+11}{4}-\frac{11}{7}+8 \leq 11+3 \)

Calculate the value by following steps: - step0: Calculate: \(\frac{\left(1+11\right)}{4}-\frac{11}{7}+8-\left(11+3\right)\) - step1: Remove the parentheses: \(\frac{1+11}{4}-\frac{11}{7}+8-\left(11+3\right)\) - step2: Add the numbers: \(\frac{1+11}{4}-\frac{11}{7}+8-14\) - step3: Add the numbers: \(\frac{12}{4}-\frac{11}{7}+8-14\) - step4: Divide the terms: \(3-\frac{11}{7}+8-14\) - step5: Calculate: \(-3-\frac{11}{7}\) - step6: Reduce fractions to a common denominator: \(-\frac{3\times 7}{7}-\frac{11}{7}\) - step7: Transform the expression: \(\frac{-3\times 7-11}{7}\) - step8: Multiply the numbers: \(\frac{-21-11}{7}\) - step9: Subtract the numbers: \(\frac{-32}{7}\) - step10: Rewrite the fraction: \(-\frac{32}{7}\) Let's solve the inequality step by step. 1. **Calculate the left side of the inequality:** \[ \frac{1 + 11}{4} - \frac{11}{7} + 8 \] - First, calculate \(1 + 11 = 12\). - Then, \(\frac{12}{4} = 3\). - Now, we have: \[ 3 - \frac{11}{7} + 8 \] - Next, convert \(3\) and \(8\) to have a common denominator with \(\frac{11}{7}\): \[ 3 = \frac{21}{7} \quad \text{and} \quad 8 = \frac{56}{7} \] - Now, combine these: \[ \frac{21}{7} - \frac{11}{7} + \frac{56}{7} = \frac{21 - 11 + 56}{7} = \frac{66}{7} \] 2. **Calculate the right side of the inequality:** \[ 11 + 3 = 14 \] 3. **Set up the inequality:** \[ \frac{66}{7} \leq 14 \] 4. **Convert \(14\) to a fraction with a denominator of \(7\):** \[ 14 = \frac{98}{7} \] 5. **Now, compare the two fractions:** \[ \frac{66}{7} \leq \frac{98}{7} \] This inequality is true since \(66 \leq 98\). Thus, the final result is: \[ \frac{66}{7} \leq 14 \]