Question

The points (3,-2) and (2, 1) are both solutions to which inequality?

Answer 1

(3, -2) and (2, 1) are solutions to the inequality y <= 3/2x - 1

How to determine the inequality?

The complete question is added as an attachment

The points are given as:

(3, -2) and (2, 1)

Next, we test the points on each inequality in the list of options.

So, we have:

Option 1

y > 1/2x + 2

Substitute (3, -2) and (2, 1) for x and y

-2 > 1/2 * 3 + 2 ⇒ -2 > 3.5 -- false

2 > 1/2 * 1 + 2 ⇒ 2 > 2.5 -- false

Hence, (3, -2) and (2, 1) are not solutions to the inequality y > 1/2x + 2

Option 2

y <= 3/2x - 1

Substitute (3, -2) and (2, 1) for x and y

-2 <= 3/2 * 3 - 1 ⇒ -2 <= 3.5 -- true

1 <= 3/2 * 2 - 1 ⇒ 1 < 2 -- true

Hence, (3, -2) and (2, 1) are solutions to the inequality y <= 3/2x - 1

Option 3

y >= 4x - 2

Substitute (3, -2) and (2, 1) for x and y

-2 >= 4 * 3 - 2 ⇒ -2 >= 10 -- false

2 <= 4 * 2 - 2 ⇒ 2 <= 6 -- false

Hence, (3, -2) and (2, 1) are not solutions to the inequality y >= 4x - 2

Option 4

y < -2x + 1

Substitute (3, -2) and (2, 1) for x and y

-2 < -2 * 3 + 1 ⇒ -2 < -5 -- false

2 < -2 * 2 + 1 ⇒ 2 < -3 -- false

Hence, (3, -2) and (2, 1) are not solutions to the inequality y < -2x + 1

Read more about inequality at

brainly.com/question/24372553

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