Question

Which values are in the solution set of the inequality −23x + 13 ≥ −1 ?

Select all that apply.

(3 points)
Responses

19
19

20
20

21
21

22
22

23

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the values that are in the solution set of the inequality, we can solve the inequality for x.

−23x + 13 ≥ −1

To isolate x, we can subtract 13 from both sides of the inequality:

−23x ≥ −1 - 13
−23x ≥ -14

Finally, we can divide both sides of the inequality by -23. Remember that when we divide or multiply an inequality by a negative number, the direction of the inequality sign must be reversed:

x ≤ -14 / -23
x ≤ 14/23

The solution set of the inequality is all the values of x that are less than or equal to 14/23.

Therefore, the values in the solution set are 19, 20, 21, 22, and 23.

Answer choices 19, 20, 21, 22, and 23 are all correct.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the solution set of the inequality −23x + 13 ≥ −1, we need to isolate x.

−23x + 13 ≥ −1

First, subtract 13 from both sides to get:

−23x ≥ −14

Next, divide both sides by −23. Remember that when we divide or multiply by a negative number, we need to reverse the inequality sign:

x ≤ 14/23

Therefore, any value of x that is less than or equal to 14/23 is in the solution set.

Now let's determine which values from the given options are less than or equal to 14/23.

Option 19: 19 is not less than or equal to 14/23.
Option 20: 20 is not less than or equal to 14/23.
Option 21: 21 is not less than or equal to 14/23.
Option 22: 22 is not less than or equal to 14/23.
Option 23: 23 is not less than or equal to 14/23.

Therefore, none of the given options are in the solution set.

Answer 3

[AI-generated answer — Explain Bot]

To determine which values are in the solution set of the inequality −23x + 13 ≥ −1, we need to find the values of x that satisfy the inequality.

First, let's solve the inequality step by step:

Step 1: Subtract 13 from both sides of the inequality:
−23x + 13 - 13 ≥ −1 - 13
−23x ≥ −14

Step 2: Divide both sides of the inequality by −23. When dividing by a negative number, we need to flip the direction of the inequality.
x ≤ −14 ÷ −23
x ≤ 14/23

Therefore, the values of x that satisfy the inequality are x ≤ 14/23.

Now, let's check which of the given options are within the solution set:

19 is not within the solution set as 19 is greater than 14/23.
20 is not within the solution set as 20 is greater than 14/23.
21 is not within the solution set as 21 is greater than 14/23.
22 is not within the solution set as 22 is greater than 14/23.
23 is not within the solution set as 23 is greater than 14/23.

None of the given options are within the solution set of the inequality.