Algebra Reasoning NEW

Algebra Reasoning

​Inequalities

​Inequality: a mathematical sentence that uses symbols such as <, >, ≤, ≥, or ≠ to compare quantities.

​x = 5: "x equals 5" so x is 5

​

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 ...

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

​Translating inequalities into Algebra

Multiple Choice

If x has to be at least 24, which inequality would represent that?

• x < 24

• x > 24

• x ≤ 24

• x ≥ 24

Multiple Choice

If x has to be at most 24, which inequality would represent that?

• x < 24

• x > 24

• x ≤ 24

• x ≥ 24

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

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

​EXAMPLE

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.

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

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

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

​EXAMPLE

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

x + y ≥ 6

GRAPH

GRAPH

150x + 100y ≤ 900

GRAPH

x ≥ 1

Hotspot

Where do all three inequalities overlap?

Open Ended

Can Jimmy stay at the Hyatt for 2 nights and the Coral Reef for 5 nights under these constraints?

Explain mathematically

Math Response

How many integer solutions are there for this scenario?

Type answer here

Correct Answer: 11

Deg^°

Rad

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