Question

Solve Absolute Value Inequalities with “greater than”

$\left|x-5\right|>-2$

Short answer

The solution of the inequality is$\left(-\infty ,\infty \right)$

Step-by-step solution

Given information

We are given a inequality$\left|x-5\right|>-2$

We write the equivalent compound inequality

$x-5<2$and$x-5>-2$

Solve the inequality

$x<7$and$x>3$

The solution of the inequality is 

$\left(-\infty ,\infty \right)$

We plot the graph of the inequality

Conclusion

The solution of the inequality is$\left(-\infty ,\infty \right)$

The graph of the inequality is