Chapter 3.7, Problem 4P

To determine

Tograph:The find the solutions of inequality $\left|2x+4\right|\ge 5$ , and graph them.

Answer to Problem 4P

The solutions of inequality $\left|2x+4\right|\ge 5$ is $x\le -4.5$ and $x\ge 0.5$ , their graph is shown in Figure-1.

Explanation of Solution

Given information:

The inequality $\left|2x+4\right|\ge 5$ .

Conceptused:

  $\left|2x+4\right|\ge 5\Rightarrow \left|2x+4\right|\le -5$

Calculations:

The given inequality is $\left|2x+4\right|\ge 5$ or $\left|2x+4\right|\le -5$ .

Now, $\left|2x+4\right|\le -5\Rightarrow -(-5)\le \left(2x+4\right)\le -5$

  $\Rightarrow 5\le 2x+4\le -5$

  $\Rightarrow 5-4\le 2x\le -5-4$  Subtracting 4

  $\Rightarrow 1\le 2x\le -9$

  $\Rightarrow \frac{1}{2}\le x\le \frac{-9}{2}$

  $\Rightarrow 0.5\le x\le -4.5$

Thus, $x\le -4.5$ and $x\ge 0.5$ is the solution of the inequality $\left|2x+4\right|\ge 5$ .

The graph of solutions is shown in Figure-1 here.

  

Conclusion:

The solution of inequality $\left|2x+4\right|\ge 5$ is $x\le -4.5$ and $x\ge 0.5$ , their graph is shown in Figure-1.