Algebra-2

To solve the inequality |2n + 4| - 3 < 5, we will first isolate the absolute value expression and then break it down into two separate inequalities.

Step 1: Isolate the Absolute Value

We start with:

|2n + 4| - 3 < 5

Adding 3 to both sides:

|2n + 4| < 8

 

Step 2: Rewrite the Absolute Value Inequality

The expression |2n + 4| < 8 means:

-8 < 2n + 4 < 8

 

Step 3: Solve the Inequalities

For the left part of the inequality:

−8 < 2n + 4

Subtracting 4 from both sides:

−12 < 2n

Dividing by 2:

−6 < n or n > −6

 

For the right part of the inequality:

2n + 4 < 8

Subtracting 4 from both sides:...