Question

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

Answer 1

Answer:

4 < x < 12

Step-by-step explanation:

Given:

$\displaystyle \large{9|x-8| < 36}$

Divide both sides by 9:

$\displaystyle \large{|x-8| < 4}$

Theorem:

For $\displaystyle \large{|x-a| < b}$, since absolute is less than a constant, the interval or solution is:

$\displaystyle \large{-b < x-a < b}\\\displaystyle \large{-b+a < x < b+a}$

Therefore:

$\displaystyle \large{|x-8| < 4 \to -4 < x-8 < 4}\\\displaystyle \large{-4+8 < x < 4+8}\\\displaystyle \large{4 < x < 12}$

Therefore, the solution is 4 < x < 12

Answer 2

Answer:

4 < x < 12

Step-by-step explanation:

9|x - 8| < 36

Divide both sides by 9:

|x - 8| < 4

Solution 1

(x - 8) < 4

Add 8 to both sides:

x < 12

Solution 2

-(x - 8) < 4

-x + 8 < 4

Subtract 8 from both sides:

-x < -4

Divide both sides by -1 (remembering to change the direction of the sign):

x > 4

Therefore, the solution to the inequality is   4 < x < 12