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  1. Which ordered pairs are solutions to the inequality –3x + y ≥ 7?

(–2, –3)

(–1, 8)

(0, 7)

(1, 9)

(3, 18)

  1. Jude is placing boxes on a shelf that holds up to 80 lb. He has x small boxes that weigh 5 lb each and y large boxes that weigh 12 lb each. Jude needs at least 4 small boxes on the shelf.

Which inequalities model the situation?


Choose exactly three answers that are correct.


5x + 12y < 80

5x + 12y ≤ 80


x > 4

x ≥ 4

y > 0

y ≥ 0

Verified Answer :

JcAlmighty

Q1. The answers are (–1, 8), (0, 7), (3, 18)

–3x + y ≥ 7
Let's go through all choices:

(–2, –3) 
(-3) (-2) + (-3) ≥ 7
6 - 3 ≥ 7
3 ≥ 7       INCORRECT

(–1, 8) 
(-3) (-1) + 8 ≥ 7
3 + 8 ≥ 7
11 ≥ 7       CORRECT

(0, 7) 
(-3) 0 + 7 ≥ 7
0 + 7 ≥ 7
7 ≥ 7       CORRECT

(1, 9) 
(-3) 1 + 9 ≥ 7
-3 + 9 ≥ 7
6 ≥ 7       INCORRECT

(3, 18) 
(-3) 3 + 18 ≥ 7
-9 + 18 ≥ 7
9 ≥ 7       CORRECT



Q2. The answers are:
5x + 12y ≤ 80
x ≥ 4
y ≥ 0

x - small boxes
y - large boxes

He has x small boxes that weigh 5 lb each and y large boxes that weigh 12 lb each on a shelf that holds up to 80 lb:
5x + 12y ≤ 80

Jude needs at least 4 small boxes on the shelf: x ≥ 4

Let's check if y can be 0:
5x + 12y ≤ 80
5x + 12 0 ≤ 80
5x + 0 ≤ 80
5x ≤ 80
x ≤ 80 / 5
x ≤ 16

x ≥ 4 can include x ≤ 16

So, y can be 0: y ≥ 0

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