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.
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
1 answer