Solve and graph the absolute value inequality: |2x+1| greater than or equal to 5

x ≥ 2                  or            x  ≤ -2

Step-by-step explanation:

|2x+1|≥5

There is a positive and negative solution.  When we take the negative solution we flip the inequality.

2x+1 ≥5     or     2x+1 ≤-5

Subtract 1 from each side

2x+1-1 ≥5-1          2x+1-1 ≤-5-1

2x  ≥ 4                  2x  ≤- 4

Divide by 2

2x/2 ≥ 4/2                  2x/2  ≤- 4/2

x ≥ 2                  or            x  ≤ -2

Step-by-step explanation:

Solution One

2x + 1 ≥ 5                 Subtract 1 from both sides.

2x + 1 - 1 ≥ 5 - 1

2x ≥ 4                       Divide by 2

2x/2 ≥ 4/2    

x ≥ 2

Solution Two

2x + 1 ≤ - 5               Subtract 1 from both sides.

2x + 1 - 1 ≤ -5 -1              

2x ≤ -6                      Divide by 2

2x/2 ≤ -6/2

x ≤ -3

Which part is the graphical solution?

The pink colored area because the absolute value turns it positive.

you can't solve x because it is 2 linear equation and you only have one equation