Chapter 6.1, Problem 52E

To determine

To solve the inequality $\frac{2}{3}x+9\le \frac{17}{2}$ .

Answer to Problem 52E

  $x\le -\frac{3}{4}$

Explanation of Solution

Given:

Inequality: $\frac{2}{3}x+9\le \frac{17}{2}$

Calculation:

Consider given inequality $\frac{2}{3}x+9\le \frac{17}{2}$ ,

  $\begin{array}{c}\frac{2}{3}x+9\le \frac{17}{2}\\ \frac{2x+27}{3}\le \frac{17}{2}\text{ [}\because \text{Taking Least common factor]}\\ \left(2x+27\right)·2\le 17·3\\ \left(2x+27\right)·2\le 51\\ 4x+54\le 51\\ 4x+54-54\le 51-54\text{ [}\because \text{Subtracting 54 on both sides]}\\ 4x\le -3\\ \frac{4x}{4}\le -\frac{3}{4}\text{ [}\because \text{Dividing 4 on both sides]}\\ x\le -\frac{3}{4}\end{array}$

Conclusion:

Therefore, $x\le -\frac{3}{4}$ is the required solution.