Question

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

Answer 1

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