18
Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities like equations. Be wary of closed verses open circles when graphing. Must reverse the inequality sign if multiplying or dividing by a negative number!

Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Embed Size (px)

Citation preview

Page 1: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Goal:

I can Graph and Solve multi-step linear inequalities.

What do we know already?

2.5– Solving Inequalities with Variables on Both Sides

Solve inequalities like equations.

Be wary of closed verses open circles when graphing.

Must reverse the inequality sign if multiplying or dividing by a negative number!

Page 2: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

When solving for variables in inequalities, treat the inequality as though it were an equation and use inverse operations to solve for the variable (like before with equations!).

Solve: 3x + 4 > 13

Two (or more) Step Inequalities - Review

- 4 -4

3x > 93 9

3 3

x

x > 3

Page 3: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Now solve: 2x < -10 + 3x

Remember to flip the sign IF you multiply or divide by a negative number.

Variables on BOTH Sides

- 3x -3x

-x < -10

x > 10

Page 4: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Examples

Solve x < 3x + 8. Graph the solution.

- 3x -3x

-2x < 8

x > -4

-8 -7 -6 -5 -4 -3 -2 -1 0

Page 5: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Examples

Solve -3x + 1 < 3x + 21. Graph the solution.

+ 3x +3x

1 ≤ 6x + 21 - 21 - 21

-20 ≤ 6x

6 6

-6 -5 -4 -3 -2 -1 0 1 2

Page 6: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

My Turn – Special Answers

Solve 2(x + 3) < 5 + 2x . Graph the solution.

-6 -5 -4 -3 -2 -1 0 1 2

2x + 6 ≤ 5 + 2x

- 2x - 2x

6 ≤ 5

Not a true statement

NO SOLUTION!!!!

Page 7: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

My Turn – Special Answers

Solve x + 5 > x + 3 . Graph the solution.

-x -x

5 ≥ 3

True Statement!

INFINITE SOLUTIONS

Page 8: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

The Daily Info charges a fee of $650 plus $80 per week to run an ad. The People’s Paper charges $145 per week. For how many weeks will the total cost at Daily Info be less expensive than the cost at People’s Paper?

x = # of weeksDaily Info People’s Paper

<

-80x -80x

650 < 65x

65 65

10 < x

x > 10

So, after 10 weeks the Daily Info will be LESS Expensive

Page 9: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Example – Linear Inequality - Guided

You see an advertisement for instructions on how to tie flies for fishing. The instruction book costs $15.00. The cost of materials for each fly is 15 cents. You plan to sell each fly for 58 cents, and you want to make a profit of at least 200 dollars. How many flies will you need to tie and sell?

Question – What is profit?

Question – What are we trying to solve for in this problem?

Question – What other key information do we know?

Page 10: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Examples

Solve -x + 1 < 3x + 21. Graph the solution.

Page 11: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Your Turn

Solve 4x + 1 > 7x + 6. Graph the solution.

Page 12: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Your Turn

Solve 5t + 1 < -2t - 6. Graph the solution.

Page 13: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Examples

Solve 6(1 - x) < 3x . Graph the solution.

Page 14: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Your Turn

Solve 1.6x < -0.2x + 0.9 . Graph the solution.

Page 15: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Your Turn

Solve 1.6x < -0.2x + 0.9 . Graph the solution.

Page 16: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Your Turn

Solve 2(x – 2) < -2(1 – x) . Graph the solution.

Page 17: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Quick Review

Solve inequalities just as you would equations using inverse operations.

When multiplying or dividing by a negative number, always remember to flip the sign around.

Page 18: Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities

Homework

P199, 28-48 even, 52-55, 61-64