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 equations2. 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

= 5

1.7 – Solving Absolute Value Equations and Inequalities

Think: “Which number(s) is/are 5 units away from the origin?”

x = 5

1.7 – Solving Absolute Value Equations and Inequalities

= 12

1.7 – Solving Absolute Value Equations and Inequalities

x + 4 = 12

1.7 – Solving Absolute Value Equations and Inequalities

= 15

1.7 – Solving Absolute Value Equations and Inequalities

2x + 7 = 15

1.7 – Solving Absolute Value Equations and Inequalities

Solve these equations:

|6x – 3|= 15

|2x – 8|= - 24

2|4x + 5|– 7 = 33

1.7 – Solving Absolute Value Equations and Inequalities

1.7 – 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|> 6

1.7 – Solving Absolute Value Equations and Inequalities

Meaningful/conceptual understanding of solving absolute value inequalities: Khan 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 x > c “or”

With absolute value on LEFT…• Less thAND• GreatOR than

1.7 – Solving Absolute Value Equations and Inequalities

Graph these inequalities:

|4x - 9| < 21

|3x - 2| > 18

2|-3x + 10|– 5 > 7

1.7 – Solving Absolute Value Equations and Inequalities

Graph these inequalities:

4|x + 5| > -8

4|x + 5| < 8

1.7 – Solving Absolute Value Equations and Inequalities

=Isolate absolute valueBreak up into two problemsOne problem where number is +, one problem where number is –

> or >

Break up into two problems“GreatOR” “or” problemKeep one the same, other problem with the opposite sign

< or <

“Less thAND” “and” problemWhat 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. 53-54 #29, 30, 32, 33, 41,

42, 56, 58

• Chapter 1 Review on Friday, September 7th

• Chapter 1 Test on Monday, September 10th

Homework