Algebra-2Algebra-2

Lesson 5-3 Lesson 5-3 Absolute Value InequalitiesAbsolute Value Inequalities

Quiz 1-6Quiz 1-6

x > 3 and x < 5x > 3 and x < 5

Graph the compound inequalitiesGraph the compound inequalities

1. 1.

2. 2. x x ≤≤ 3 or x > 5 3 or x > 5

QuizQuizDescribe the transformation to Describe the transformation to the parent function.the parent function.

3. 3. 32 xy

4. 4. 2)5( 2 xy

5. 5. 614 xy

23 x

33 If you can’t tell which direction the arrow goes, (If you can’t tell which direction the arrow goes, () or () or ( ) ) pick a number that is between 1 and 5 and see if it makes sense.pick a number that is between 1 and 5 and see if it makes sense.

((EnglishEnglish):): The distance between The distance between “ “some number (x)” and “+3” is some number (x)” and “+3” is greater thangreater than “2” “2”

5 1

4

Is the distance between 3 and 4 greater than 2?Is the distance between 3 and 4 greater than 2?

NO! NO! so the arrows must open outward not inward. so the arrows must open outward not inward.

XX XX

65 x2. 2. Write numbers in the for letters ‘a’, ‘b’, ‘c’, ‘d’, ‘e’Write numbers in the for letters ‘a’, ‘b’, ‘c’, ‘d’, ‘e’

Your turn: Your turn: 1. 1. Write the “Write the “English”English” version of: version of:

d

3. 3. Do the numbers ‘b’ and ‘e’ have an open circle or a solid Do the numbers ‘b’ and ‘e’ have an open circle or a solid circle?circle?

4. 4. Which direction do the arrows go?Which direction do the arrows go?

a

c

e b

23 x

33

Do you have to graph it to figure it out?Do you have to graph it to figure it out?

5 1

1x 5x

23 x23 x

Absolute Value Absolute Value INEQUALITIESINEQUALITIES

15 x

x – 5 > 1x – 5 > 1x – 5 < -1x – 5 < -1

Your turn:Your turn:

37 x5. 5. Solve for xSolve for x

6. 6. GraphGraph 23 x

32 x

22

If you can’t tell which direction the arrow goes, (If you can’t tell which direction the arrow goes, () or () or ( ) ) pick a number that is between -1 and 5 and see if it makes pick a number that is between -1 and 5 and see if it makes sense.sense.

((EnglishEnglish):): The distance between The distance between “ “some number (x)” and “+2” is some number (x)” and “+2” is LESS thanLESS than “3” “3”

5 -1

4

Is the distance between 2 and 4 LESS than 3?Is the distance between 2 and 4 LESS than 3?

yESS! yESS! so the arrows must open inward not outward. so the arrows must open inward not outward.

XX XX

15 xDo you have to graph it to figure it out?Do you have to graph it to figure it out?

6 4

4x 6x

15 x15 x

15 xDo you have to graph it to figure it out?Do you have to graph it to figure it out?

6 4

4x 6x

15 x15 x

Absolute Value Absolute Value INEQUALITIESINEQUALITIES

15 x

x – 5 < 1x – 5 < 1x – 5 > -1x – 5 > -1

Your turn:Your turn:

39 x7. 7. Solve for xSolve for x

8. 8. Solve for xSolve for x 26 x

Solving Inequalities by Solving Inequalities by GraphingGraphing

15 x5 xy 1y

For what values of ‘x’ are the y-values of For what values of ‘x’ are the y-values of

less than the y-values of:less than the y-values of:

5 xy1y

Solving Inequalities by Solving Inequalities by GraphingGraphing

15 x5 xy 1y

For what values of ‘x’ are the y-values of For what values of ‘x’ are the y-values of

less than the y-values of:less than the y-values of:

5 xy1y

64 x