Question

What is the solution (in interval notation) to the following inequality below?

-14 < -x - 8 < -4
a.) [-4, 6]
b.) [-4, 6)
c.) (-4, 6]
d.) (-4, 6)

Answer 1

To find the solution to the inequality -14 < -x - 8 < -4 in interval notation, we need to solve each inequality separately. The solution is (-4, 6).

Step-by-step explanation:

To find the solution to the inequality -14 < -x - 8 < -4 in interval notation, we need to solve each inequality separately.

We start with -14 < -x - 8. Subtracting 8 from both sides gives -6 < -x. Multiplying both sides by -1 and flipping the inequality sign gives x < 6.

Next, we solve -x - 8 < -4. Adding 8 to both sides gives -x < 4. Multiplying both sides by -1 and flipping the inequality sign gives x > -4.

Combining both solution sets, the solution to the inequality is (-4, 6). Therefore, the correct answer is d.) (-4, 6).