Given the inequality:

l 2x +1 l < 3

By definition, we can rewrite:

-3 < 2x+1 < 3

Now we will subtract -1 from all sides.

==> -4 < 2x < 2

Now we will divide by 2.

==> -2 < x < 1

Then the values of x belongs to the interval (-2, 1)

.....l......l......l**___l__l___**l......l......l......l.......

-4 -3 -2 -1 0 1 2 3 4

To draw the graph of |2x + 1| >3, remember that

|2x +1| = 2x + 1 , when 2x + 1 > 0

and -(2x + 1) when 2x + 1 < 0

So we have two inequations here.

2x + 1 > 3, for 2x + 1> 0

=> 2x > 2 and 2x > -1

x > 1 satisfies both

-(2x + 1) > 3 for 2x + 1 < 0

=> 2x + 1 < 3

=> 2x < 2 and x < -1/2

=> x < -1/2 satisfies both.

**So the required graph would have all values of x with x > 1 and x < -1/2**

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.