Solve each absolute value inequality. Graph the solution:

The correct answer is: Combining the above two solutions, we get x ≤ - 7 and x ≥ - 1

Step by step solution:
The given inequality is

2|x + 4| ≤ - 6
Dividing by 2 throughout, we get

-|x + 4 |≤ - 3
Multiplying by -1, we have

|x + 4| ≥ 3
We use the definition of , which is

For, x + 4 < 0,
We have

|x + 4| = - (x + 4) ≥ 3
Simplifying, we get

- x - 4 ≥ 3
Adding 4 on both sides, we get

x ≥ 3 + 4

Multiplying  on both sides, we have

x ≤ - 7
For We have

|x + 4|= x +  4 ≥ 3
Subtracting 4 from both sides, we get

x ≥ 3 -  4

Combining the above two solutions, we get

x ≤ - 7 and x ≥  -1
We plot the above inequality on the real line.

The points -7 and -1 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’.