Question

Solve the inequality: -12 < 1/2(4x+16) < 18.

A) x < 6
B) x > -6
C) -12 < x < 6
D) x > 6

Answer 1

After solving the inequality by first multiplying by 2, then subtracting 16, and dividing by 4, the solution is –-10 < x < 5. The solution provided in the options given with the question does not match this correct solution.

Step-by-step explanation:

To solve the inequality -12 < \frac{1}{2}(4x+16) < 18, we should first multiply each part of the inequality by 2 to eliminate the fraction:

-24 < 4x + 16 < 36

Next, we'll subtract 16 from each part:

-40 < 4x < 20

Now we divide each part by 4 to solve for x:

-10 < x < 5

Therefore, the solution to the inequality is -10 < x < 5, which is not listed in the possible answers provided. It looks like there may be an error in the options given by the question. None of the answers A to D is correct.