Solve |2x + 1| < 3 or |2x +1| > 3.   

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

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