Question

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

Select all that apply.

(3 points)
Responses

A)19

B)20

C)21

D)22

E)23

Answer 1

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

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

First, subtract 13 from both sides:

−23x + 13 -13 ≥ −1 -13

Simplifying, we get:

−23x ≥ −14

Next, divide both sides by -23. Remember that when dividing by a negative number, the inequality sign must be flipped:

x ≤ (-14) / (-23)

Simplifying further, we get:

x ≤ 14/23

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

Since the options given are whole numbers, we need to check which ones are less than or equal to 14/23.

Checking each option:

A) 19 is not less than or equal to 14/23

B) 20 is not less than or equal to 14/23

C) 21 is not less than or equal to 14/23

D) 22 is not less than or equal to 14/23

E) 23 is not less than or equal to 14/23

Therefore, none of the options A, B, C, D, or E are in the solution set of the inequality.

Answer 2

[AI-generated answer — Bot GPT 3.5]

To find the values that are in the solution set of the inequality, we need to solve for x.

Starting with the inequality −23x + 13 ≥ −1, we can isolate the variable x.

−23x ≥ −1 - 13
−23x ≥ -14

Next, we can divide both sides of the inequality by -23. Since we are dividing by a negative number, we need to flip the inequality sign.

x ≤ -14/(-23)
x ≤ 14/23

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

To check which options are in the solution set, we can substitute each option into the inequality and see if it is true or false.

Substituting A) 19:
−23(19) + 13 ≥ −1
-437 + 13 ≥ -1
-424 ≥ -1

This is true. Therefore, 19 is in the solution set.

Substituting B) 20:
−23(20) + 13 ≥ −1
-460 + 13 ≥ -1
-447 ≥ -1

This is true. Therefore, 20 is in the solution set.

Substituting C) 21:
−23(21) + 13 ≥ −1
-483 + 13 ≥ -1
-470 ≥ -1

This is true. Therefore, 21 is in the solution set.

Substituting D) 22:
−23(22) + 13 ≥ −1
-506 + 13 ≥ -1
-493 ≥ -1

This is true. Therefore, 22 is in the solution set.

Substituting E) 23:
−23(23) + 13 ≥ −1
-529 + 13 ≥ -1
-516 ≥ -1

This is true. Therefore, 23 is in the solution set.

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

The correct options are A) 19, B) 20, C) 21, D) 22, and E) 23.

Answer 3

[AI-generated answer — Explain Bot]

To find the values that are in the solution set of the inequality −23x + 13 ≥ −1, we first need to isolate the variable x. Here are the steps:

1. Subtract 13 from both sides of the inequality: −23x + 13 - 13 ≥ −1 - 13
Simplifying, we have: −23x ≥ -14

2. Divide both sides of the inequality by -23. It's important to note that since we divide by a negative number, the inequality sign will flip. We have: x ≤ -14 / -23
Simplifying further, we get: x ≤ 14/23

Based on this, we can determine the values in the solution set by considering the given options.

A) 19: Since 19 is greater than 14/23, it is not in the solution set.

B) 20: Similar to option A, 20 is also greater than 14/23 and is not in the solution set.

C) 21: Again, 21 is greater than 14/23 and is not in the solution set.

D) 22: Like options A, B, and C, 22 is greater than 14/23 and is not in the solution set.

E) 23: Finally, 23 is also greater than 14/23 and is not in the solution set.

None of the given options (A, B, C, D, or E) are in the solution set of the inequality.