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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!
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
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
Examples
Solve x < 3x + 8. Graph the solution.
- 3x -3x
-2x < 8
x > -4
-8 -7 -6 -5 -4 -3 -2 -1 0
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
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!!!!
My Turn – Special Answers
Solve x + 5 > x + 3 . Graph the solution.
-x -x
5 ≥ 3
True Statement!
INFINITE SOLUTIONS
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
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?
Examples
Solve -x + 1 < 3x + 21. Graph the solution.
Your Turn
Solve 4x + 1 > 7x + 6. Graph the solution.
Your Turn
Solve 5t + 1 < -2t - 6. Graph the solution.
Examples
Solve 6(1 - x) < 3x . Graph the solution.
Your Turn
Solve 1.6x < -0.2x + 0.9 . Graph the solution.
Your Turn
Solve 1.6x < -0.2x + 0.9 . Graph the solution.
Your Turn
Solve 2(x – 2) < -2(1 – x) . Graph the solution.
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.
Homework
P199, 28-48 even, 52-55, 61-64