Question

What is the solution to | x - 9| - 3 < 1

Answer 1

5 < x < 13... so i say c

Explanation:

To solve the inequality | x - 9| - 3 < 1, we can add 3 to both sides of the inequality to isolate the absolute value term:

| x - 9| < 4

To remove the absolute value, we can consider two cases:

Case 1: x - 9 ≥ 0, or x ≥ 9

In this case, the inequality becomes:

x - 9 < 4

Simplifying this inequality, we get:

x < 13

Therefore, any value of x that is greater than or equal to 9 and less than 13 satisfies the inequality in this case.

Case 2: x - 9 < 0, or x < 9

In this case, the inequality becomes:

-(x - 9) < 4

Simplifying this inequality, we get:

x > 5

Therefore, any value of x that is less than 9 and greater than 5 satisfies the inequality in this case.

Putting both cases together, we get:

5 < x < 13

So the solution to the inequality is all values of x that are strictly between 5 and 13.

Answer 2

5 < x < 13

Explanation:

Solving for x:

| x - 9| - 3 < 1

Add 3 to each side.

| x - 9| - 3+3 < 1+3

| x - 9| < 4

Separating into two inequalities.

x-9 < 4 and x-9 > -4

Solving

x < 13 and x > 5

Putting back together.

5 < x < 13