Solve each absolute value inequality. Graph the solution

The correct answer is: Combining the above two solutions, we get x ≤ - 4 and x ≥ 4

Step by step solution:
The given inequality is

2|4x|-7 ≥ 25
Adding 7 both sides, we get

2|4x| ≥ 25 + 7

Dividing by 2 throughout, we get

We use the definition of , which is

For, 4x < 0,
We have

|4x|= - 4x ≥ 16
Dividing by 4 throughout, we get

Multiplying  on both sides, we have

X ≤ - 4

For, 4x ≥ 0,
We have

|4x|= 4x ≥ 16
Dividing by 4 throughout, we get

Combining the above two solutions, we get

 
We plot the above inequality on the real line.

The points -4 and 4 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. We could also simplify the inequality further before solving it by dividing by 4 throughout.