Creating and Solving Inequalities
Presentation
•
Mathematics
•
8th Grade
•
Practice Problem
•
Hard
+1
Standards-aligned
Carmea Dixon
Used 9+ times
FREE Resource
12 Slides • 12 Questions
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8.PAR.3.3 Create and solve linear equations and inequalities in one variable within a relevant, real-life application.
8.PAR.3.4 Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.
8.PAR.3.5 Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solution based on the contextual, mathematical situation.
3
Review from Last Week.......
Answer the next question with your group
4
Multiple Choice
There were approximately 11,000 students enrolled at Western Carolina last year. If this figure goes up by about 225 students each year, how many years will it take the enrollment to reach 20,000 students?
10 years
20 years
30 years
40 years
5
(1 minute)
What is the difference between an equation and an inequality?
6
(Equation vs Inequality)
An EQUATION shows the EQUAL value of TWO expressions. An equation has ONE solution, NO solution, or INFINITELY MANY solutions.
An INEQUALITY shows that an expression is LESSER THAN or MORE THAN the other. An inequality has MORE THAN one solution.
7
When graphing inequalities:
GREATER THAN or LESS THAN has an OPEN circle.
Greater than or EQUAL TO or Less than or EQUAL TO has a CLOSED circle.
8
Multiple Choice
Which graph represents the following inequality:
x < 5
9
Multiple Choice
Which inequality matches the graph.
x <−4.5
x >−4.5
x ≤−4.5
x≥−4.5
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One-Step Inequalities
(Add or Subtract)
ADD or SUBTRACT to ISOLATE the variable.
SOLVE by performing the INVERSE operation.
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One-Step Inequalities
(Multiply or Divide-Positive Sign)
MULTIPLY or DIVIDE to ISOLATE the variable.
SOLVE by performing the INVERSE operation.
SIMPLIFY your answer.
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One-Step Inequalities
(Multiply or Divide-Negative Sign)
MULTIPLY or DIVIDE to ISOLATE the variable.
SOLVE by performing the INVERSE operation.
When MULTIPLYING or DIVIDING by a NEGATIVE number, FLIP the inequality sign.
SIMPLIFY your answer.
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Two-Step Inequalities
Step 1: ADD or SUBTRACT the CONSTANT on the side with the variable.
Step 2: MULTIPLY or DIVIDE to ISOLATE the variable.
If MULTIPLYING or DIVIDING by a NEGATIVE number, FLIP the inequality sign.
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Multiple Choice
Solve the following inequality:
3t − 12 ≤ −9
t ≥1
t≤1
t≥7
t≤7
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Multiple Choice
Solve the following inequality:
4 − 2y < 12
y >−4
y<−4
y>−8
y<−8
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Real World Inequality Word Problems
READ through the entire problem.
HIGHLIGHT the important information and KEY words that you need to solve the problem.
Identify your VARIABLES.
TRANSLATE your key words and write the INEQUALITY.
SOLVE the problem.
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Multiple Choice
200+25x≥500
500+25x≥200
500−25x≥200
500−25x≤200
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Multiple Choice
Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the maximum amount of hours she will need to babysit in order for her to buy her calculator?
5x+10≤100
5x−100≥10
10x+5≤100
5x+10≥100
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Group Work:
Practice Problems
20
Multiple Select
Jim paid a gym membership fee of $50, plus $20 per month. Jim's budget is $300, how long can he be a member at the gym?
(Select all that apply)
9 months
1 year
1.25 years
1.5 years
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Multiple Choice
Penelope is going to be a vendor at the carnival. She spent $125 for the ingredients for cotton candy and candy apples and $160 for the cases of apples. She's going to sell each item for $6. How many bags of cotton candy and candy apples must she sell to make a profit?
58
59
47
48
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Multiple Choice
Mrs. Scott decided that she would spend at least $150 to buy a jacket and a skirt. If the price of the jacket was $30 more than 3 times the price of the skirt, which inequality represents the lowest possible price of the skirt?
s≥60
s≤60
s≥40
s≤40
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Multiple Choice
The dance committee hired a DJ for the spring dance. The DJ charges $125 per hour in addition to $75 for the set-up fee. The committee wants to keep the total cost under $450. Which is the maximum amount of hours the DJ will play at the dance?
4 hours
2 hours,
59 minutes
3 hours, 45 minutes
3 hours
24
Poll
As a group, rate your understanding of Creating and Solving Linear Inequalities after completing this lesson:
4 - We understand how to create and solve linear inequalities and teach a peer how to do it.
3 - We understand how to create and solve linear inequalities.
2 - We understand how to create and solve linear inequalities with the help of our group.
1 - We need more help on how to create and solve linear inequalities.
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