Solve for x.1. 6(2x – 3) – 2(6x + 1) = 10x

2. 15 + 2x – 4 = 9x + 11 – 7x

Solve for h. 3.

Warm – up #4

1. 6(2x – 3) – 2(6x + 1) = 10x12x – 18 – 12x – 2 = 10x - 20 = 10x

10 10x = –2

Warm – up #4 Solutions

2. 15 + 2x – 4 = 9x + 11 – 7x 11 + 2x = 11 + 2x

-11 -11 2x = 2x

-2x - 2x0 = 0

ALWAYS TRUE!!! Infinite

Solution!!

Warm – up #4 Solutions

3. Solve for h.

Warm – up #4 Solutions

Lesson 1 – 5 Solving Inequalities Day 1

Algebra II

To solve & graph inequalities

To write & solve compound inequalities

Learning Objective

Open circle on the number lineDoes NOT include the #

> Greater than< Less than

Closed circle on the number lineINCLUDES the #

Greater than or equal toLess than or equal to

x > 7 x is greater than 7

x 7 x is greater than or equal to 7

Writing & Graphing Inequalities

x < 7 x is less than 7

x 7 x is less than or equal to 7

Writing & Graphing Inequalities

Inequalities Words

Less Than < Less Than or Equal to Is fewer than

Is less than Is at most Is no more than

Is at maximum

Inequalities WordsGreater Than > Greater Than or

Equal to Is more than Is larger than Is at least

Is no less than Is at minimum

5 fewer than a number is at least 12

x – 5 12

The quotient of a number and 3 is no more than 15

Write an Inequality from a Sentence

ALWAYS FLIP THE

INEQUALITY SIGN

WHEN YOU

DIVIDE BY – #

1. -3(2x – 5) + 1 4-6x + 15 + 1 4 -6x + 16 4 - 16 - 16 -6x - 12

-6 - 6 x 2

Solve & Graph Inequalities

FLIP!!!

2. -2(x + 9) + 5 < 3-2x – 18 + 5 < 3 -2x – 13 < 3 +13 +13 -2x < 16

-2 - 2 x >-8

Solve & Graph Inequalities

FLIP!!!

3. -2(3x + 1) > -6x + 7-6x – 2 > - 6x + 7 +2 +2 -6x > -6x + 9

+6x +6x 0 > 9

NEVER TRUE! No Solution

Solve & Graph Inequalities

4. 5(2x – 3) – 7x < 3x + 810x – 15 – 7x < 3x + 8 3x – 15 < 3x + 8 -3x -3x

- 15 < 8ALWAYS TRUE! Infinite Solutions

Solve & Graph Inequalities

5. 4(2x – 3) > 8(x + 1)8x – 12 > 8x + 8

-8x -8x - 12 > 8

NEVER TRUE! No Solution

Solve & Graph Inequalities

Compound Inequality – join two inequalities with the word and or or

“And” compound inequality – Find all values of the variable that make BOTH inequalities true. Need overlap

“Or” compound inequality – Find all values of the variables that make at least one of the inequalities true

6. 7 < 2x + 1 and 3x 18 -1 -1 & 3 3

6 < 2x & x 6 2 2 3 < x x > 3 and x 6 3 < x 6

Solve & Graph Inequalities

7. 5 3x - 1 and 2x < 12 +1 +1 & 2 2

6 3x & x < 6 3 3 2 x x 2 and x < 6 2 x < 6

Solve & Graph Inequalities

8. 5< x + 1 < 13 -1 -1 - 1

4 < x < 12

Solve & Graph Inequalities

Read: x + 1 is greater than 5 AND less than 13

9. 7 + x 6 or 8 + x < 3 -7 -7 -8 -8

x -1 or x < - 5

NOT -5> x -1 NOR -1 x <- 5

Solve & Graph Inequalities

00

10. 7x + 3 > 11 or 4x – 1 < -13 -3 -3 +1 +1

7x > 8 or 4x < -12 7 7 4 4

x > or x < -3

Solve & Graph Inequalities

00

11. 16 < 5x + 1 or 3x + 9 < 6 -1 -1 -9 -9

15 < 5x or 3x < -3 5 5 3 3

3 < x or x < -1x > 3 or x < -1

Solve & Graph Inequalities

00

Your friend solved the problem as shown.

What was his error?

Ticket Out the Door

Assignment:

Pg. 38 #15 – 23 odd, 45 – 49 odd