Solve the inequality: -2(2x - 4) ≤ 4(2 - x).
A) x ≤ 0
x ≤ 0
B) x ≤ 4
x ≤ 4
x ≤ 8
x ≤ 8
C) All Real Numbers
All Real Numbers
D) No Solution
To solve the inequality, we will distribute and simplify both sides:
-2(2x - 4) ≤ 4(2 - x)
-4x + 8 ≤ 8 - 4x
Next, we will combine like terms:
-4x + 8 + 4x ≤ 8 - 4x + 4x
8 ≤ 8
The inequality simplifies to 8≤8 which is true for all real numbers.
Therefore, the solution is:
C) All Real Numbers
To solve the inequality, we will simplify both sides and then isolate the variable x.
Let's start by simplifying both sides of the inequality:
-2(2x - 4) ≤ 4(2 - x)
Distribute the -2 on the left side and the 4 on the right side:
-4x + 8 ≤ 8 - 4x
Now, combine like terms:
-4x + 8 ≤ -4x + 8
The x terms cancel out, and we are left with:
8 ≤ 8
Since 8 is equal to 8, this means that the inequality is true for all real numbers. Hence, the solution is:
C) All Real Numbers
To solve the inequality -2(2x - 4) ≤ 4(2 - x), we need to simplify both sides of the inequality and isolate the variable x.
Starting with the left side, distribute the -2 to both terms inside the parentheses:
-2 * 2x = -4x
-2 * (-4) = 8
So, the left side of the inequality becomes -4x + 8.
Now, let's work on the right side. Distribute the 4 to both terms inside the parentheses:
4 * 2 = 8
4 * (-x) = -4x
The right side of the inequality becomes 8 - 4x.
Now, we can rewrite the inequality as:
-4x + 8 ≤ 8 - 4x.
Notice that we have -4x on both sides. By subtracting -4x from both sides, we eliminate it:
-4x - 4x + 8 ≤ 8 - 4x - 4x.
This simplifies to:
8 ≤ 8.
Since 8 is equal to 8, this means that the inequality is true for all real numbers. Therefore, the solution to the inequality is C) All Real Numbers.