Warm-ups: Simplify or Evaluate the following

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Presentation transcript:

Warm-ups: Simplify or Evaluate the following 25 − 1 2 8 3 2 ∙ 8 5 2 16 1 4 𝑥 3 4 ∙𝑥 9 4 ∙𝑥 3 𝑏 1 3 3 5

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 7.1-7.7 Assignment Due Friday, 4/25: A# 7.71: Page 425 #12-28, 32-38 even MUST SHOW WORK TO RECEIVE CREDIT

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 _________________.

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!

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

PRACTICE#1: Solve Radical Equations Solve each equation. d. 4− 7−𝑦 1 2 =0 c. 4𝑥+1 =3

Example #2: Solve a Cube Root Equation

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

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

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