Solve the inequality and give the solution set.
-|4x + 1| + 3

Question

Solve the inequality and give the solution set.
-|4x + 1| + 3 < -3

Quizplus · Accepted Answer

First, we need to understand the meaning of absolute value. |4x + 1| means the distance of 4x + 1 from 0 on the number line. This value can never be negative.

Now, let's solve the inequality:

|4x + 1| + 3 < -3

Subtracting 3 from both sides,

|4x + 1| < -6

Since an absolute value can never be negative, there is no real solution to this inequality. Therefore, the solution set is empty or null.

The correct choice is D, which indicates an empty solution set. |4x + 1| + 3 < -3

|4x + 1| < -6

But an absolute value can never be negative. Hence, there are no solutions to this inequality.

Therefore, the answer is D, none of the given choices.

Solve the Inequality and Give the Solution Set