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
To solve the inequality -23x + 13 ≥ -1, we need to isolate the variable on one side of the inequality symbol.
We can start by subtracting 13 from both sides:
-23x + 13 - 13 ≥ -1 - 13
-23x ≥ -14
Next, we can divide both sides of the inequality by -23. Because we are dividing by a negative number, the inequality symbol will reverse:
x ≤ -14/-23
x ≤ 14/23
So, the solution set is x ≤ 14/23.
Based on the given answer choices, none of them is equivalent to 14/23. Therefore, none of the given values are in the solution set of the inequality.
To find the values in the solution set of the inequality −23x + 13 ≥ −1, we need to solve the inequality for x.
Starting with the given inequality:
−23x + 13 ≥ −1
We want to isolate x, so let's begin by subtracting 13 from both sides of the inequality:
−23x ≥ −1 - 13
−23x ≥ −14
Next, to solve for x, we'll divide both sides of the inequality by −23. It's important to note that whenever we divide or multiply both sides of an inequality by a negative number, we need to reverse the direction of the inequality sign:
x ≤ (-14)/(-23)
Simplifying further:
x ≤ 14/23
So, the solution set for the inequality is x ≤ 14/23.
Now, let's check which values in the options (19, 20, 21, 22, and 23) satisfy this inequality:
For x = 19: 19 ≤ 14/23 (Not true)
For x = 20: 20 ≤ 14/23 (Not true)
For x = 21: 21 ≤ 14/23 (Not true)
For x = 22: 22 ≤ 14/23 (Not true)
For x = 23: 23 ≤ 14/23 (Not true)
None of the given values (19, 20, 21, 22, and 23) satisfy the inequality x ≤ 14/23.
Therefore, none of the options are in the solution set of the given inequality.
To find the values in the solution set of the given inequality −23x + 13 ≥ −1, we need to solve the inequality for x.
First, let's isolate the variable x by subtracting 13 from both sides of the inequality:
−23x + 13 - 13 ≥ −1 - 13
Simplifying, we get:
−23x ≥ −14
Now, to get x alone, we divide both sides of the inequality by −23. However, when dividing an inequality by a negative number, the direction of the inequality sign must be flipped. So, we have:
x ≤ −14 / −23
Simplifying further, we get:
x ≤ 14/23
Therefore, the solution set of the inequality −23x + 13 ≥ −1 is all values of x that are less than or equal to 14/23.
None of the given options (19, 20, 21, 22, or 23) are less than or equal to 14/23. So, none of them are in the solution set of the inequality.