Solve the inequality: -2(2x - 4) ≤ 4(2 - x).(1 point)
Responses
x ≤ 0
x ≤ 0
x ≤ 4
x ≤ 4
x ≤ 8
x ≤ 8
All Real Numbers
All Real Numbers
No Solution
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
23
24
To solve the inequality −23x + 13 ≥ −1, we need to isolate the variable x. Here's how you can do that:
1. Subtract 13 from both sides to eliminate it on the left side of the inequality:
−23x + 13 - 13 ≥ −1 - 13
−23x ≥ −14
2. Divide both sides by -23 to solve for x:
x ≤ (-14) / (-23)
Simplifying the right side:
x ≤ 14/23
Therefore, the solution to the inequality is x ≤ 14/23.
Now, let's determine which values are in the solution set of the inequality. To do this, we can evaluate each option and check if it satisfies the inequality:
1. Substitute 19 into the inequality:
−23(19) + 13 ≥ −1
−437 + 13 ≥ −1
−424 ≥ −1 (True)
2. Substitute 20 into the inequality:
−23(20) + 13 ≥ −1
−460 + 13 ≥ −1
−447 ≥ −1 (True)
3. Substitute 21 into the inequality:
−23(21) + 13 ≥ −1
−483 + 13 ≥ −1
−470 ≥ −1 (True)
4. Substitute 22 into the inequality:
−23(22) + 13 ≥ −1
−506 + 13 ≥ −1
−493 ≥ −1 (True)
5. Substitute 23 into the inequality:
−23(23) + 13 ≥ −1
−529 + 13 ≥ −1
−516 ≥ −1 (True)
From the above evaluations, all the options: 19, 20, 21, 22, and 23 satisfy the inequality −23x + 13 ≥ −1. Therefore, all of them are in the solution set.
To solve the inequality −23x + 13 ≥ −1, we need to isolate the variable x.
Let's begin by subtracting 13 from both sides of the inequality:
−23x + 13 - 13 ≥ −1 - 13
−23x ≥ -14
Next, divide both sides of the inequality by -23. Since we are dividing by a negative number, we need to reverse the inequality sign:
x ≤ -14 / -23
Simplifying further:
x ≤ 14/23
Thus, the solution set for the inequality is x ≤ 14/23.
Therefore, none of the given options (19, 20, 21, 22, 23) are in the solution set.