Schedule: Class Announcements Homework Check/Questions 1.7 Notes Video and Practice Begin Homework Algebra 2

1.7 – Solving Absolute Value Equations and Inequalities Objectives: 1.Solve absolute equations 2.Solve absolute inequalities Vocabulary: absolute value Algebra 2

What is absolute value? 1.7 – Solving Absolute Value Equations and Inequalities The distance a number is from 0 (the origin) on a number line. Positive? Negative? We can’t have negative distance!

Simplify these expression: 1.7 – Solving Absolute Value Equations and Inequalities |-5| |7| |-4 – 7| |2(3 – 8)| Think: “How many units is -5 away from 0?” |-5|= 5

= – Solving Absolute Value Equations and Inequalities Think: “Which number(s) is/are 5 units away from the origin?”

x = – Solving Absolute Value Equations and Inequalities

= – Solving Absolute Value Equations and Inequalities

x + 4 = – Solving Absolute Value Equations and Inequalities

= – Solving Absolute Value Equations and Inequalities

2x + 7 = – Solving Absolute Value Equations and Inequalities

Solve these equations: |6x – 3|= 15 |2x – 8|= |4x + 5|– 7 = – Solving Absolute Value Equations and Inequalities

Summary: For absolute value equations… Isolate the absolute value Split the problem up into two: Positive Negative

Graph these inequalities: |x|< 5 |x|< 4 |x|> 2 |x|> – Solving Absolute Value Equations and Inequalities

Meaningful/conceptual understanding of solving absolute value inequalities: Khan AcademyKhan Academy 1.7 – Solving Absolute Value Equations and Inequalities

Absolute value inequality “shortcuts”: |x|< c, then -c < x < c “and” |x|> c, then x c “or” With absolute value on LEFT… AND Less thAND OR GreatOR than With absolute value on LEFT… AND Less thAND OR GreatOR than 1.7 – Solving Absolute Value Equations and Inequalities

Graph these inequalities: |4x - 9| < 21 |3x - 2| > 18 2|-3x + 10|– 5 > – Solving Absolute Value Equations and Inequalities

Graph these inequalities: 4|x + 5| > -8 4|x + 5| < – Solving Absolute Value Equations and Inequalities

= Isolate absolute value Break up into two problems One problem where number is +, one problem where number is – > or > Break up into two problems “GreatOR”  “or” problem Keep one the same, other problem with the opposite sign < or < “Less thAND”  “and” problem What you do to the middle, you must do to the left and right sides 1.7 – Solving Absolute Value Equations and Inequalities

Due tomorrow: pgs #29, 30, 32, 33, 41, 42, 56, 58 Chapter 1 Review on Friday, September 7 th Chapter 1 Test on Monday, September 10 th Homework