Solve each absolute value inequality. Graph the solution:

The correct answer is: Combining the above two solutions, we get x ≤ - 7 and x ≥ 2

Step by step solution:
The given inequality is

|2 x + 5| ≥ 9
We use the definition of , which is

For, 2x + 5 < 0,
We have

|2x + 5| = - (2x + 5) ≥ 9
Simplifying, we get

-2x – 5 ≥ 9
Adding 5 on both sides, we get

-2x ≥ 9 + 5

Dividing by 2 on both sides, we get

-x ≥ 7
Multiplying  on both sides, we have

X ≤ - 7

For, x ≥ 0,
We have

|2x + 5| = 2x + 5 ≥
Subtracting 5 from both sides, we get

2x ≥ 9 - 5

Dividing by 2 throughout, we get

X ≥ 2
Combining the above two solutions, we get

X  ≤ - 7 and x ≥ 2
We plot the above inequality on the real line.

The points -7 and 2 are included in the graph.
 

The given inequality contains only one variable. So, the graph is plotted on one dimension, which is the real line. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.