Algebra-2

To solve the inequality |3n + 1| - 5 < 0, follow these steps:

Step 1: Isolate the absolute value

Starting from the original inequality:

|3n + 1| - 5 < 0

Add 5 to both sides:

|3n + 1| < 5

 

Step 2: Rewrite the absolute value inequality

The inequality |3n + 1| < 5 can be rewritten as:

-5 < 3n + 1 < 5

 

Step 3: Split into two inequalities

Now we can split this compound inequality into two parts:

3n + 1 < 5

3n + 1 > -5

 

Step 4: Solve each part

For the first part:

3n + 1 < 5

Subtract 1 from both sides:

3n < 4

Now divide by 3:

n <

 

For the second part:

3n + 1 > -5

Subtract 1 from both sides:

3n > -6

Now divide by 3:

n > -2

 

Step 5: Combine the results

Combining both inequalities gives:

-2 < n <