Chapter 6.3, Problem 81STP

To determine

To evaluate:

The value of the given number

Answer to Problem 81STP

The value of given operation is $x\le -\frac{2}{3}\text{or}x\ge 2$ .

Explanation of Solution

Given:

The equation

  $\left|-3x+2\right|\ge 4$

Concept used:

Replace the inequality sign and sketch the graph of the resulting equation (use a dashed line for < or > and a solid line for $\le or\ge$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

Calculation:

The order of operation

  $\left|-3x+2\right|\ge \mathrm{4.......................}\left(1\right)$

Rewrite the inequality

  $\begin{array}{l}-4\ge -3x+2\ge 4\\ -4-2\ge -3x\ge 4-2\\ -6\ge -3x\ge 2\\ 2\le x\le -\frac{2}{3}\\ x\le -\frac{2}{3}\text{or}x\ge 2\end{array}$