what are the answers
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
x ≥ -12
All values greater than or equal to -12 would be in the solution set.
To solve the inequality -2(2x - 4) ≤ 4(2 - x), we can follow these steps:
Step 1: Distribute the coefficients on both sides of the inequality.
-4x + 8 ≤ 8 - 4x
Step 2: Combine like terms on both sides of the inequality.
-4x + 4x ≤ 8 - 8
Step 3: Simplify the equation.
0 ≤ 0
From this equation, we can see that the inequality is always true, regardless of the value of x. This means that the solution set includes all real numbers.
In the second question, to find the values in the solution set of the inequality -23x + 13 ≥ -1, we can follow these steps:
Step 1: Subtract 13 from both sides of the inequality.
-23x ≥ -14
Step 2: Divide both sides of the inequality by -23. Since we are dividing by a negative number, the inequality sign will flip.
x ≤ (-14) / (-23)
Step 3: Simplify the equation.
x ≤ 14/23
So, the solution set includes any value of x that is less than or equal to 14/23.
From the given options, the values that are in the solution set are:
- 19
- 20
- 21
- 22
Therefore, the correct options are:
- 19
- 20
- 21
- 22
To solve the inequality -23x + 13 ≥ -1, follow these steps:
1. Subtract 13 from both sides of the inequality:
-23x + 13 - 13 ≥ -1 - 13
-23x ≥ -14
2. Divide both sides of the inequality by -23, remembering to flip the inequality sign when dividing by a negative number:
-23x / -23 ≤ -14 / -23
x ≤ 14/23
Therefore, the solution to the inequality is x ≤ 14/23.