Chapter 3.8, Problem 22P

Solve each inequality. Write the solutions as either the union or intersection of two sets.

$|2w-5|\ge 0$

To determine

To solve the inequality $\left|2w-5\right|\ge 0$ and write the solution as either union or intersection of two sets.

Answer to Problem 22P

The solution of inequality $\left|2w-5\right|\ge 0$ is $\left(-\infty ,0\right)\cup \left[0,\infty \right)$

Explanation of Solution

Given information :

Given inequality $\left|2w-5\right|\ge 0$

Given inequality $\left|2w-5\right|\ge 0$

Since absolute value is always zero or positive,

Thus, $\left|2w-5\right|\ge 0$ holds for all values of $w$ from $-\infty \text{to}\infty .$

Now we express the interval $\left(-\infty ,\infty \right)$ as either union or intersection of two sets.

Let $\left(-\infty ,\infty \right)=\left(-\infty ,0\right)\cup \left[0,\infty \right)$

Hence, the solution of inequality $\left|2w-5\right|\ge 0$ is $\left(-\infty ,0\right)\cup \left[0,\infty \right)$