Chapter 6.3, Problem 82STP

To determine

To evaluate:

The value of the given number

Answer to Problem 82STP

The value of given operation is no solution .

Explanation of Solution

Given:

The equation

  $\left|2x-8\right|-4\le -6$

Concept used:

Replace the inequality sign 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.

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

  $\left|2x-8\right|-4\le -\mathrm{6.......................}\left(1\right)$

Rewrite the inequality

  $\begin{array}{l}\left|2x-8\right|-4\le -6\\ \left|2x-8\right|\le -6+2\\ \left|2x-8\right|\le -2\end{array}$

Since the absolute value cannot be less than a negative value, the inequality has no solution .