
Algebra Reasoning NEW
Presentation
•
Mathematics
•
12th Grade
•
Hard
Standards-aligned
Christopher Gassler
Used 3+ times
FREE Resource
9 Slides • 12 Questions
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Inequality: a mathematical sentence that uses symbols such as <, >, ≤, ≥, or ≠ to compare quantities.
x < 5: "x is less than 5" so x is 4, 3, 2, 1 ,0, -1, -2 ...
x ≤ 5: "x is less than or equal to 5" so x is 5, 4, 3, 2, 1 ,0, -1, -2 ...
x > 5: "x is greater than 5" so x is 6, 7, 8, 9, 10, 11, 12 ...
x ≥ 5: "x is greater than or equal to 5" so x is 5, 6, 7, 8, 9, 10, 11, 12 ...
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Match
Match the following inequalities with their translations.
x < 5
x > 5
x < -5
x > -5
x is less than five
x is greater than five
x is less than negative five
x is greater than negative five
x is less than five
x is greater than five
x is less than negative five
x is greater than negative five
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Multiple Choice
If x has to be at least 24, which inequality would represent that?
x < 24
x > 24
x ≤ 24
x ≥ 24
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Multiple Choice
If x has to be at most 24, which inequality would represent that?
x < 24
x > 24
x ≤ 24
x ≥ 24
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Multiple Choice
If y represents how many days you want to stay at Disneyworld, and you want to stay there for at least 5 days, which inequality would represent that?
y < 5
y > 5
y ≤ 5
y ≥ 5
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Multiple Choice
For any given month, if x represents how much you pay for your phone bill and y represents how much you pay for your car insurance, and you don't want those bills to be more than $135, which inequality would represent that?
x + y ≤ 135
x + y ≥ 135
x - y ≤ 135
x - y ≥ 135
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Jimmy wants to vacation in Jamaica for at least 6 days. He wants to spend no more than $900 on hotels while he’s there. He wants to stay at the Hyatt Resort for at least 1 night and at the Coral Reef Hotel for the remainder of his stay. The Hyatt Resort costs $150 per night, and the Coral Reef Hotel is $100 per night.
The paragraph has the facts / parameters / contraints of the situation.
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Multiple Choice
Given Information: Jimmy Jawn wants to spend no more than $900 on hotels while vacationing for at least 6 days in Jamaica. He wants to stay at the Hyatt Resort for at least 1 night and at the Coral Reef Hotel for the remainder of his stay. The Hyatt Resort costs $150 per night, and the Coral Reef Hotel is $100 per night.
Question: If x represents days at the Hyatt Resort and y represents days at the Coral Reef Hotel, which inequality represents the number of days he can stay at the hotels?
x + y ≤ 6
x + y ≥ 6
x - y ≤ 6
x - y ≥ 6
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Multiple Choice
Given Information: Jimmy Jawn wants to spend no more than $900 on hotels while vacationing for at least 6 days in Jamaica. He wants to stay at the Hyatt Resort for at least 1 night and at the Coral Reef Hotel for the remainder of his stay. The Hyatt Resort costs $150 per night, and the Coral Reef Hotel is $100 per night.
Question: If x represents days at the Hyatt Resort and y represents days at the Coral Reef Hotel, which inequality represents the amount of money he can spend?
150x + 100y ≤ 900
100x + 150y ≤ 900
150x - 100y ≤ 900
100x + 150y ≤ 900
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Multiple Choice
Given Information: Jimmy Jawn wants to spend no more than $900 on hotels while vacationing for at least 6 days in Jamaica. He wants to stay at the Hyatt Resort for at least 1 night and at the Coral Reef Hotel for the remainder of his stay. The Hyatt Resort costs $150 per night, and the Coral Reef Hotel is $100 per night.
Question: If x represents days at the Hyatt Resort and y represents days at the Coral Reef Hotel, which inequality represents the number of days he wants to spend at the Hyatt Resort?
x ≤ 1
x ≥ 1
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Jimmy wants to vacation in Jamaica for at least 6 days. He wants to spend no more than $900 on hotels while he’s there. He wants to stay at the Hyatt Resort for at least 1 night and at the Coral Reef Hotel for the remainder of his stay. The Hyatt Resort costs $150 per night, and the Coral Reef Hotel is $100 per night.
The following represent the systems of inequalities representing Jimmy’s vacation constraints; where x represents days at the Hyatt Resort and y represents days at the Coral Reef Hotel.
x + y ≥ 6
x ≥ 1
150x + 100y ≤ 900
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x + y ≥ 6
GRAPH
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GRAPH
150x + 100y ≤ 900
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GRAPH
x ≥ 1
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Hotspot
Where do all three inequalities overlap?
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Open Ended
Can Jimmy stay at the Hyatt for 2 nights and the Coral Reef for 5 nights under these constraints?
Explain mathematically
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Math Response
How many integer solutions are there for this scenario?
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Multiple Choice
If Jimmy decided he wanted to extend his stay at the Hyatt to at least 2 nights, the overall solutions would:
Increase
Descrease
Remain unchanged
Show answer
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