1. Warm-ups: Simplify or Evaluate the following
25 − 1 2 ∙
𝑥 ∙𝑥 ∙𝑥 3 𝑏

2. Section 7.7 Solving Radical Equations and Inequalities
Class notes from Thurs 4/24
By the end of this section, you will be able to:
Define radical equation; extraneous solution; radical inequality;
Solve equations containing radicals;
Solve inequalities containing radicals.
Chapter 7 TEST
Tues 4/29
Sections
Assignment Due Friday, 4/25:
A# 7.71: Page 425 #12-28, even
MUST SHOW WORK TO RECEIVE CREDIT

3. New vocabulary Radical Equation:
Equations with ___________ that have ____________ in the ___________________.
Extraneous Solution:
A number obtained as a ______________ that does not satisfy the _______________.
Radical Inequality:
Inequalities with ___________ that have ____________ in the _________________.

4. Steps to solving a radical equation
Isolate the radical on one side of the equals sign.
Raise each side of the equation to a power equal to the index of the radical. This eliminates the radical!
Solve for the variable.
Check your solution to ensure it is not extraneous!

5. Example #1: Solve Radical Equations
Solve each equation.
b. 𝑥+15 =5+ 𝑥
a. 5= 𝑥−2 −1

6. PRACTICE#1: Solve Radical Equations
Solve each equation.
d. 4− 7−𝑦 =0
c. 4𝑥+1 =3

7. Example #2: Solve a Cube Root Equation

8. PRACTICE #2: Solve a Cube Root Equation
d. 3 𝑥−4 =3

9. Example #3: Solve a Radical Inequality
b. 4𝑥−4 −2<4

10. PRACTICE #3: Solve a Radical Inequality
b. 𝑏+12 − 𝑏 >2