Checking Solutions for Inequalities

Write an inequality for this situation:
You are driving, and the maximum speed limit is 55.

• s < 55

• s > 55

• s ≤ 55

• s ≥ 55

Mr. Gomez gets a notice from the bank when the amount in his checking account drops below $20. Which represents an amount that will require the bank to send a notice?

• $18

• $19

• $20

• $21

• $22

You must spend at least $10 at the grocery store to get a free reusable shopping bag. Which inequality represents the amount you need to spend to get a free shopping bag?

• x<10

• x>10

• x>10

• x<10

When the following inequality is graphed, what will it look like?

y>-1

• open circle

• closed circle

When the following inequality is graphed, what will it look like?

r < -12.97

• open circle

• closed circle

When do you "flip the inequalities sign"?

• When you add or subtract a negative

• When it's a 1-step problem

• When you multiply or divide a negative

• When it's a 2-step problem

-3x ≤ 18

• x ≤ -6

• x ≤ 6

• x ≥ 6

• x ≥ -6

Which of the following points is a solution to the inequality y>3x+4?

• (0, 5)

• (3, 4)

• (1, 2)

• (2, 3)

Answer explanation

To solve the inequality y > 3x + 4, substitute the points. For (0, 5): 5 > 3(0) + 4, which is true. For (3, 4): 4 > 3(3) + 4 is false. For (1, 2) and (2, 3), both are false. Thus, (0, 5) is the only solution.

How do you determine if a point is a solution to a two-variable inequality?

• Graph the inequality and find the intersection point.

• Substitute the point into the inequality and check if the statement is true.

• Choose any random point and assume it is a solution.

• Check if the point lies on the boundary line only.

Answer explanation

To determine if a point is a solution to a two-variable inequality, substitute the point into the inequality. If the resulting statement is true, then the point is a solution. This method directly verifies the point's validity.

For the inequality 5x-2y>15, which point is a solution?

• (4, -1)

• (1, 4)

• (5, 10)

• (2, 3)

Answer explanation

To check which point satisfies the inequality 5x - 2y > 15, substitute each point. For (4, -1): 5(4) - 2(-1) = 20 + 2 = 22 > 15. Thus, (4, -1) is a solution. The other points do not satisfy the inequality.