Algebra-2

To solve the inequality 4 - |x + 1| < 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:

4 - |x + 1| < 2

Subtracting 4 from both sides gives:

-|x + 1| < -2

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

|x + 1| > 2

 

Step 2: Rewrite the Absolute Value Inequality

The expression |x + 1| > 2 translates into two inequalities:

x + 1 < −2 or x + 1 > 2

 

Step 3: Solve the Inequalities

For the left part of the inequality:

x + 1 < -2

Subtracting 1 from both sides gives:

x < -3

 

For the ...