## Tuesday, November 22, 2016

### High School Math Solutions – Inequalities Calculator, Radical Inequalities

Last post, we went over how to solve absolute value inequalities. For today’s post, we will talk about how to solve radical inequalities. Solving radical inequalities is easier than solving absolute value inequalities and require fewer steps. Let’s see the steps on how to solve these inequalities.

Steps:
1. Isolate the square root
2. Check that the inequality is true (i.e. not less than 0)
3. Find the real region for the square root, (i.e. see when the expression inside square root igreater than or equal to 0)
4. Simplify and compute the inequality
5. Combine the ranges

Let’s see how to do one example step by step.

\sqrt{5+x}-1<3

Step 1: Isolate the square root

\sqrt{5+x}<4

Step 2: Check that the inequality is true

Yes, this inequality is true the radical is not less than 0.

Step 3: Find the real region for the square root

5+x≥0

x≥-5

Step 4: Simplify and compute the inequality

\sqrt{5+x}<4

(\sqrt{5+x})^2<4^2

5+x<16

x<11
Step 5: Combine the ranges

x≥-5 and x<11

-5≤x<11

That wasn’t too difficult. Let’s see some more examples.