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
Expanding both sides of the inequality, we have:
-4x + 8 ≤ 8 - 4x.
Now let's simplify the inequality:
-4x + 8 ≤ -4x + 8.
The two sides of the inequality are equal, so this inequality holds for all real numbers. The correct answer is: All Real Numbers.
To solve the inequality -2(2x - 4) ≤ 4(2 - x), let's start by simplifying both sides:
-2(2x - 4) ≤ 4(2 - x)
Simplifying the left side:
-2(2x - 4) = -4x + 8
Simplifying the right side:
4(2 - x) = 8 - 4x
Now we can rewrite the inequality:
-4x + 8 ≤ 8 - 4x
-4x + 4x ≤ 8 - 8
0 ≤ 0
The inequality 0 ≤ 0 is always true, which means that the solution to the original inequality is all real numbers.
Therefore, the correct response is: All Real Numbers.
To solve the inequality -2(2x - 4) ≤ 4(2 - x), we can start by distributing the factors on both sides of the inequality:
-4x + 8 ≤ 8 - 4x
Next, we can simplify the expression by bringing like terms together:
-4x + 4x ≤ 8 - 8
Since the -4x and 4x terms cancel each other out, we are left with:
0 ≤ 0
This expression is always true, no matter the value of x. Therefore, the solution to the inequality is "All Real Numbers".