Linear Inequalities Using Desmos

Solve 24 > -3r > -9 

• -8 < r < 3
• -8 > r > 3
• r > - 8 and r > 3 
• r > -8 or r < 3

x + 8 < 3 or - 8x < -40 

• x > -5 or x < 5
• x < -5 and x > 5
• x < -5 or x > 5 
• x > -5 and x < 5 

Solve:  -3 ≤ 2x - 1 ≤ 5

• -1 ≤ x ≤ 3
• -1 < x < 3
• 1 < x < 3
• 1 ≤ x ≤ 3

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.

Which inequality represents the situation?

• x + y ≤ 8

• x + y > 8

• 2x + 3y ≤ 6

• x + y ≤ 10

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18

• x + y ≤ 6

• x + y ≤ 9

• 3x + 2y ≤ 18

You graph using Desmos.com and get the following graph. Which are vertices of the feasible region?

• (0, 0), (0, 6),

  (6, 2), (8, 0)

• (0, 0), (6, 0),

  (2, 6), (0, 8)

Objective quantity:

30x + 50y

Corner Points: (0, 0) (8, 0) (6, 2) (0, 6)

What is the maximum profit?

• 300

• 280

• 400

• 240

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective quantity?

• 30x + 50y
• 50x + 30y

If the vertices of the feasible region are (0,0) (2,5) (6,2) and (4,4) which coordinate maximizes an objective function of P=2x+3y

• (0,0)

• (2,5)

• (6,2)

• (4,4)

Lea needs at least $240 to buy new headphones. She has already saved $30. She earns $14 per car that she washes.

What is the least number of cars she can wash to buy the headphones?

Write the inequality to the problem.

• 14x+30 ≥ 240

• 14x+30 ≤ 240

• 30x+14 ≥ 240

• 30x+14 ≤ 240