1. Write the inequality that represents “The product of 6 and a number is less than 20”

2. Solve & Graph-5(2x-1) + 3 < -2

3. 3(4x + 2) + x 1 + 13x

Warm – up #5

1. 6x < 202. -5(2x-1) + 3 < -2 -10x + 5 + 3 < -2

-10x + 8 < -2 - 8 - 8-10x < -10-10 -10

x > 1

Warm – up #5 Solutions

FLIP!!!

3. 3(4x + 2) + x 1 + 13x 12x + 6 + x 1 + 13x

13x + 6 1 + 13x -13x -13x

6 1NEVER TRUE!!!

No Solution!!

Warm – up #5 Solutions

Lesson 1 – 5 Solving Inequalities Day 2

Algebra II

To solve & graph inequalities

To write & solve compound inequalities

Learning Objective

ALWAYS FLIP THE

INEQUALITY SIGN

WHEN YOU

DIVIDE BY – #

1. 10+x > 7+2x or 4x–9 > x+6 -7 -7 +9 +9 3 + x > 2x or 4x > x + 15

-x -x -x -x3 > x or 3x > 15

3 3x < 3 or x > 5

Solve & Graph Inequalities

2. x–7 < -x+9 and 6+7x > x+6 +x +x -x -x

2x – 7 < 9 & 6 + 6x > 6 +7 +7 -6 -62x < 16 & 6x > 02 2 6 6x < 8 and x > 0 0 < x < 8

Solve & Graph Inequalities

3. 4x – 3 > 13 and 4x + 10 ≥ 22 +3 +3 - 10 -10

4x > 16 & 4x ≥ 124 4 4 4x > 4 and x ≥ 3Need OVERLAP because

ANDx > 4

Solve & Graph Inequalities

4. 1 and 2x 8(8) 1(8) 2 2

x 8and x 4Need OVERLAP because

AND x 4

Solve & Graph Inequalities

5. -8x + 2 > - 22 and 9x – 7 > 47

-2 -2 +7 +7 -8x > -24 and 9x > 54

-8 -8 9 9x < 3 and x > 6

Not Possible!!No Solution

Solve & Graph Inequalities

FLIP!!!

6. -8 < x – 9 < - 12

+9 +9 +9 1 < x < -3

Not Possible!!No Solution

Solve & Graph Inequalities

7. 10 – 5x 25 or 2x – 9 < -21 -10 -10 +9 +9

-5x 15 or 2x < -12 -5 -5 2 2x ≤ - 3 or x < -6Either OR Don’t need

overlapx ≤ -3

Solve & Graph Inequalities

FLIP!!!

8. x + 8 > 2 or 7x – 5 > 51 - 8 - 8 + 5 +5

x > - 6 or 7x > 56 7 7x > - 6 or x > 8Either OR Don’t need

overlapx > - 6

Solve & Graph Inequalities

9. -5+x 5+6x or 7x–2 8x+1 +5 +5 +2 +2

x 10 + 6x or 7x 8x + 3 -6x - 6x -8x -8x

-5x 10 or -x 3-5 -5 -1 -1x -2 or x -3

All Real Numbers

Solve & Graph Inequalities

FLIP!!!

10. -77 -9x + 4 < -41

-4 - 4 -4 -81 -9x < -45

-9 -9 -9 9 x > 5

5 < x 9

Solve & Graph Inequalities

FLIP!!!

11. 10 – 9x 10 or 3x + 2 26 -10 -10 - 2 -2

-9x 0 or 3x 24 -9 -9 3 3

x 0 or x 8

Solve & Graph Inequalities

FLIP!!!

12. 10+6x > 22 and 5x+3 < 8 -10 -10 -3 -3

6x > 12 & 5x < 5 6 6 5 5

x > 2 and x < 1No Solution

Solve & Graph Inequalities

13. 8 + 6x > -16 or 9x + 1 > 91 -8 -8 -1 -1

6x > - 24 or 9x > 90 6 6 9 9

x > - 4 or x > 10x > - 4

Solve & Graph Inequalities

14. 3x – 4 > 5 and -3x – 9 < 21 + 4 +4 +9 +9

3x > 9 and -3x < 30 3 3 - 3 -3

x > 3 and x > -10x > 3

Solve & Graph Inequalities

A contractor estimated that her expenses for a construction project would be between $700,000 and $750,000. She has already spent $496,000. How much more can she spend and remain within her estimate?

Explain how you came up with your answer

Ticket Out the Door

Assignment:

Pg. 38 #36 – 43, 59 - 65