Question

What is the solution to 9|x – 8| < 36?

4 < x < 12
x < –4 or x > 12
x > –12 or x < 8
–4 < x < 8

Answer 1

The answer is A. 4 < x < 12.

Explanation:

By isolating the absolute value expression:

9|x – 8| < 36

|x – 8| < 4

Break this down into two separate inequalities, one without the absolute value:

x - 8 < 4 or x - 8 > -4

Simplifying each one:

x < 12 or x > 4

Now we can combine these two inequalities with an "and" statement, since the value of x must satisfy both inequalities:

4 < x < 12

Therefore, the solution to the inequality 9|x – 8| < 36 is 4 < x < 12.