Question

Which of the following is the solution to the inequality below?

-6(4 - x) - 4(x + 1)
A) x ≥ 2
B) x = 10
C) x = 6
D) x ≤ 2

Answer 1

The solution to the inequality -6(4 - x) - 4(x + 1) involves distributing both terms, combining like terms, and solving for x. The result is x ≥ 14, which does not match any of the provided options, indicating there may be an error in the question or additional information needed.

Step-by-step explanation:

The inequality given is -6(4 - x) - 4(x + 1). To solve this, distribute both terms within the parentheses. This gives us:

• -6 * 4 = -24
• -6 * -x = 6x
• -4 * x = -4x
• -4 * 1 = -4

Now, combine the like terms:

-24 + 6x - 4x -4 which simplifies to:

2x - 28

To find the solution for x, we set the inequality to be greater or equal to zero:

2x - 28 ≥ 0

Now, we add 28 to both sides:

2x ≥ 28

Then, we divide by 2:

x ≥ 14

However, there seems to be an error in the given options as none of them match the result. If the inequality is actually intended to equal something other than zero, then additional information would be needed to proceed.