Question

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

Answer 1

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?

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

Answer 2

x ≥ 2 or x ≤ -2

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