In this section, square root inequalities will be solved using the table on a calculator. A calculator is needed for this section.

Solve using a graphing calculator.

Enter the information into your calculator as if you were going to graph the two sides of the inequality as separate functions under Y1 and Y2.

Just like when you look for the parts of the graph that were above and below y = 3, you need to compare the two y-columns. Look for where the y-coordinate in the square root function is above, below, and equal to 3.

Click on the blanks to reveal the answers

Why does it say “ERROR” in the Y₁ column for x = - 2? Interactive button. Assistance may be required. __________ If you substitute in any x-value less than -1, you will get an imaginary number which is not in the domain of the square root function.

Which colored area contains the solutions? Interactive button. Assistance may be required. __________ Yellow

Why? Interactive button. Assistance may be required. __________ The inequality symbol is < and the yellow area shows I-values that are less than 3.

How do you know that x cannot be less than -1? Interactive button. Assistance may be required. __________ When x = -1, then y = 0. If x < -1, then the radicand becomes negative which makes the y-value imaginary.

Is -1 included in the solution set? Interactive button. Assistance may be required. __________ Yes

Why or why not? Interactive button. Assistance may be required. __________ When you substitute x = -1 in, you get 0 < 3, which is true

Is 2 included in the solution set? Interactive button. Assistance may be required. __________ No

Why or why not? Interactive button. Assistance may be required. __________ Because the inequality is <. It would be included if it was ≤

What is the solution to the inequality? Interactive button. Assistance may be required. __________ -1 ≤ x < 2