Linear Inequalities, solve & give interval notations, show on number line:| 2x+1 | < 3

Question

Linear Inequalities:

 

Solve, & give interval notations, show on number line:

 

| 2x+1 | < 3

 

 

 If I solved it correctly, I got x<1, please correct me if wrong. How would I show it on a number line and what would be the interval notations? Thank you.

Answer 1

Either (2x+1) is negative        Or        (2x+1) is positive

 

2x+1<0                                           2x+1>0

 

2x<-1                                              2x>-1                                           

x<-½                                                x> -½

 

____________•________________________________________

                     -½

 

The entire number line, to the left of the point -½ and to the right of -½ or all real numbers, are solutions.
                   

Answer 2

| 2x+1 | < 3

 

2x+1 <  3                   and         -(2x+1) <3

 

2x< 2                                         -2x-1<3

                                                    -2x<4

x< 1                                              x>-2

 

 

                

so x < 1   and  x>-2          

 

-2  < x < 1

 

Interval notation                     

 

(-2,1)

Answer 3

The absolute value of a negative number is positive.  The absolute value of a positive number is positive.  Therefore, we set the inequality as

 

2x + 1 < 3          or          2x + 1 > -3

 

2x < 2                or          2x > -4

 

  x < 1                or           x > -2

 

 

The solution is   -2 < x < 1

 

In interval notation       (-2, 1)