Solve: |x| + 5 > 8

Question

A. - 3 < x < 3

B.- 13 < x < 13

C.x < - 13 or x > 13

D.x < - 3 or x > 3

Answer 1

To solve the inequality |x| + 5 > 8, we can start by subtracting 5 from both sides of the inequality:

|x| + 5 - 5 > 8 - 5

|x| > 3

Now, we can split the inequality into two cases:

Case 1: x is positive or zero
In this case, the absolute value of x is x, so the inequality becomes:

x > 3

Case 2: x is negative
In this case, the absolute value of x is -x, so the inequality becomes:

-x > 3

We can multiply both sides of this inequality by -1, but since we are multiplying by a negative number, we must flip the inequality sign:

x < -3

Putting these two cases together, we have the solution:

x < -3 or x > 3

Therefore, the correct choice is D. x < -3 or x > 3.