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
To solve the inequality, let's simplify each side separately.
On the left side, we have:
-2(2x - 4) = -4x + 8
On the right side, we have:
4(2 - x) = 8 - 4x
Now, let's substitute these values back into the inequality:
-4x + 8 ≤ 8 - 4x
We can see that -4x and -4x cancel each other out, so we are left with:
8 ≤ 8
This inequality is true for all real numbers, so the answer is:
All Real Numbers
To solve the inequality -2(2x - 4) ≤ 4(2 - x), we need to simplify each side of the inequality and then isolate the variable.
First, let's simplify the left side by distributing the -2:
-2(2x - 4) = -4x + 8
Next, let's simplify the right side by distributing the 4:
4(2 - x) = 8 - 4x
Now, let's rewrite the inequality with the simplified expressions:
-4x + 8 ≤ 8 - 4x
We can see that the variable term (-4x) cancels out on both sides, leaving us with:
8 ≤ 8
This inequality is always true, meaning the inequality holds for all real numbers.
Therefore, the solution to the inequality is "All Real Numbers."
To solve the inequality -2(2x - 4) ≤ 4(2 - x), let's simplify it step by step:
Step 1: Distribute the -2 and the 4 on each side of the inequality,
-4x + 8 ≤ 8 - 4x.
Step 2: Combine like terms,
-4x + 4x ≤ 8 - 8.
Step 3: Simplify,
0 ≤ 0.
Step 4: Since 0 is always less than or equal to 0, the inequality is true for all real numbers.
Therefore, the solution to the inequality -2(2x - 4) ≤ 4(2 - x) is "All Real Numbers".