Chapter 3.3, Problem 36E

To determine

To solve: the inequality.

Answer to Problem 36E

  $x\ge 2.5$

Explanation of Solution

Given information:

  $\left|5-x\right|\le x$

Calculation:

The outcomes of the given equality can be either of the two shown below.

  $5-x\le x$..........(1)

  $5-x\ge -x$..........(2)

Solve inequality (1) as follows:

  $\begin{array}{c}5-x\le x\\ 5-x+x\le x+x\left[\text{Add }x\text{ on both the sides}\right]\\ 5\le 2x\\ \frac{5}{2}\le \frac{2}{2}x\left[\text{Divide both the sides by 2}\right]\\ 2.5\le x\\ \therefore x\ge 2.5\end{array}$

Solve inequality (2) as follows:

  $\begin{array}{l}5-x\ge -x\\ 5-x+x\ge -x+x\left[\text{Add }x\text{ on both sides}\right]\\ 5\ge 0\\ \therefore \text{Not possible}\end{array}$

Thus, the solution of given inequality is $x\ge 2.5$ .