Question

Which inequality describes all the solutions to -6(2 + 4x) + 4 > 80?

a) x ≥ 4/5
b) x^2 - 4x ≥ -11/3
c) x ≤ 4/5
d) x ≤ -11/3

Answer 1

d) x ≤ -11/3. To find the solution to the inequality -6(2 + 4x) + 4 > 80, we must first distribute, simplify, and then solve for x. After doing this, we find that the solution to the inequality is x ≤ -11/3, which corresponds to option d).

Step-by-step explanation:

To solve the inequality -6(2 + 4x) + 4 > 80, first we distribute -6 to the terms inside the parentheses:

-6 * 2 - 6 * 4x + 4 > 80

-12 - 24x + 4 > 80

-24x - 8 > 80

Now, we add 8 to both sides of the inequality:

-24x > 88

Next, we divide both sides by -24, remembering to reverse the inequality sign because we're dividing by a negative number:

x < -88/24

Reducing the fraction:

x < -11/3

Therefore, the correct answer is d) x ≤ -11/3.