Solve each absolute value inequality. Graph the solution

The correct answer is: Combining the above two solutions, we get -6 < x < 2

Step by step solution:
The given inequality is

2|2x + 4|+10 > - 6
Subtracting 10 from both sides, we get

 |2x + 4|> - 6 - 10

Dividing by -2 throughout, we get

|2x+ 4|< 8
We use the definition of , which is

For,  We have

|2x + 4|= -(2x + 4) < 8
Multiplying  on both sides, we have

2x + 4 > -8
Subtracting 4 from both sides, we get

2x  > -  8- 4

Dividing by 2 throughout, we get

X > - 6

Or

-6 < x

For, 2x + 4 ≥ 0,
We have

|2x + 4|=2x + 4 < 8
Subtracting 4 from both sides, we get

2x < 8 - 4

Dividing by 2 throughout, we have

X < 2
Combining the above two solutions, we get

-6 < x < 2
We plot the above inequality on the real line.

The points -6 and 2 are not 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’.