Algebra-2

To solve the inequality 8 - |x + 3| > 2, we will first isolate the absolute value and then analyze the resulting expressions.

Step 1: Isolate the Absolute Value

Starting with the original inequality:

8 - |x + 3| > 2

Subtracting 8 from both sides gives:

-|x + 3| > -6

Multiplying both sides by -1 (and flipping the inequality):

|x + 3| < 6

 

Step 2: Rewrite the Absolute Value Inequality

The expression |x + 3| < 6 translates into two inequalities:

-6 < x + 3 < 6

 

Step 3: Solve the Inequalities

For the left part of the inequality:

−6 < x + 3

Subtracting 3 from both sides gives:

−9 < x or x > −9

 

For the right part o...