Framing/writing linear inequalities in two variables

Given the following equation, which information would you need to state to help you graph?

• a value, vertex, additional points

• -y < 2x - 3

• boundary line, points on boundary line

• 
• x-intercept and y-intercept

• f(x)= - |x + 2| - 1

• slope and y-intercept

• 2x + 3y = 24

Directions - For the scenario, identify the key components, then create an inequality to represent the situation. 

​To grow his ranch, a rancher is purchasing some bulls, which cost $3,200 apiece, and some cows, which cost $640 apiece. He doesn't want to spend more than $28,000 at this time.

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

​x = the number of bulls

​y = the number of cows

Which inequality written in standard form represents this scenario?

When creating a linear inequality, what is the third step?

• Find the total

• Identify the inequality for the total

• Identify the variables and the quantity associated (x = & y =)

• Write the inequality

 $f\left(x\right)\ge\ 1-\frac{1}{3}\left|x-3\right|$  Select the correct graph that matches.  

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Justin charges $11 to mow a small lawn and $26 to mow a large lawn. He would like to make at least $130.

Write an inequality that describes the situation.

Let x = # of small lawns mowed and

Let y = # of large lawns mowed

• 11x + 26y ≥ 130

• 11x + 26y > 130

• 11x + 26y ≤ 130

• 11x + 26y < 130

2 - A student is buying hot chips and sodas from the corner store. She can choose any combination of chips and sodas, and she does not want to spend more than $20. If hot chips cost $2.50 each and sodas costs $1.75 each, which inequality represents all possible combinations

of x hot chips and y sodas?

• A. 2.5x + 1.75y ≥ 20

• B. 2.5x + 1.75y ≤ 20

• C. 2.5x + 1.75y < 20

• D. 1.75x + 2.5y ≥ 20

Which inequality matches the scenario:
The sum of 5x and 3x is at most 80.

• 5x + 3x + 80
• 5x + 3x = 80
• 5x + 3x ≤ 80
• 5x + 3x ≥ 80

Harrison's crew team needs to raise at least $3,000 for their trip to the state championships. A sponsor generously donated hot dogs and cans of soda for the team to sell at each school sporting event. The crew team members will sell hot dogs for $2 each and soda for $1 each. What inequality can be used to calculate how many hot dogs, x, and sodas, y, Harrison's team needs to sell to have enough money for the trip?

• x + y ≥ 3000

• 2x + y ≤ 3000

• 2x - y ≥ 3000

• 2x + y ≥ 3000

Aleris is sending a fancy organic fruit basket to her grandma for her birthday. Apples cost RM3 and oranges cost RM2. Aleris can spend no more than RM24 on the gift.

Write an inequality that describes the situation.

Let x = # of apples

Let y = # of oranges

Aleris ingin menyediakan sebakul buah-buahan yang organik untuk meraihkan hari jadi neneknya. Harga sebiji RM3 dan sebiji oren RM2. Aleris membelanja tidak melebihi RM24 ke atas buah-buahan itu.

Tulis satu ketaksamaan yang menggambarkan situasi diberi.

Katakan x = # epal dibeli

Katakan y = # oren dibeli

• 3x + 2y < 24

• 3x + 2y > 24

• 3x + 2y ≤ 24

• 3x + 2y ≥ 24

It takes Sarah 2 hours to make small purses (x) and 3 hours to make big purses(y). She can work for no more than 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18

• x + y ≤ 6

• x + y ≤ 9

• 3x + 2y ≤ 18