solve the following inequality algebraically. |x + 9| < 6

Explanation:

Step1: Remove absolute - value

The inequality $|a|\lt b$ ($b > 0$) is equivalent to $-b\lt a\lt b$. So, $|x + 9|\lt6$ is equivalent to $-6\lt x + 9\lt6$.

Step2: Solve for $x$

Subtract 9 from all parts of the compound - inequality: $-6-9\lt x+9 - 9\lt6 - 9$. $-15\lt x\lt - 3$

Answer:

$-15\lt x\lt - 3$