Chapter 1.7, Problem 5E

To determine

To Check: The given values of S are satisfy the inequality or not.

Answer to Problem 5E

  $S=\{\sqrt{2},2,4\}$

Explanation of Solution

Given:

  $S=\{-2,-1,0,\frac{1}{2},1,\sqrt{2},2,4\}$

Inequality,

  $3-2x\le \frac{1}{2}$

Calculation, Let’s check for each value of S whether it satisfies the inequality or not,

For $x=-2$ ,

  $\begin{array}{l}3-2(-2)\le \frac{1}{2}\\ 3+4\le \frac{1}{2}\\ 7\le \frac{1}{2}\end{array}$

7 is not smaller than or equal to $\frac{1}{2}$ , so $x=-2$ does not satisfy the inequality

For $x=-1$ ,

  $\begin{array}{l}3-2(-1)\le \frac{1}{2}\\ 3+2\le \frac{1}{2}\\ 5\le \frac{1}{2}\end{array}$

5 is not smaller than or equal to $\frac{1}{2}$ So, it does not satisfy the inequality

For $x=0$

  $\begin{array}{l}3-2(0)\le \frac{1}{2}\\ 3-0\le \frac{1}{2}\\ 3\le \frac{1}{2}\end{array}$

3 is not smaller than or equal to $\frac{1}{2}$ So, it does not satisfy the inequality

For $x=\frac{1}{2}$

  $\begin{array}{l}3-2(\frac{1}{2})\le \frac{1}{2}\\ 3-1\le \frac{1}{2}\\ 2\le \frac{1}{2}\end{array}$

2 is not smaller than or equal to $x=\frac{1}{2}$ So, it doesnot satisfy the inequality

For $x=\sqrt{2}$

  $\begin{array}{l}3-2(\sqrt{2)}\le \frac{1}{2}\\ 3-2(1.41)\le \frac{1}{2}\\ 3-2.82\le \frac{1}{2}\\ 0.18\le \frac{1}{2}\end{array}$

0.18 is smaller than $\frac{1}{2}$ So, it satisfies the inequality

For $x=2$

  $\begin{array}{l}3-2(2)\le \frac{1}{2}\\ 3-4\le \frac{1}{2}\\ -1\le \frac{1}{2}\end{array}$

-1 is smaller than $\frac{1}{2}$ So, it satisfies the inequality

For $x=4$

  $\begin{array}{l}3-2(4)\le \frac{1}{2}\\ 3-8\le \frac{1}{2}\\ -5\le \frac{1}{2}\end{array}$

-5 is smaller than $\frac{1}{2}$ So it satisfies the inequality

Conclusion:

Hence, the values of S which satisfies the inequality are $\sqrt{2},2,4$