Question

# Solve each absolute value inequality. Graph the solution :

Hint:

### |x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by

First, we simplify the inequality and then solve it by considering the two cases. Then we plot the graph on the x- axis, or the real line R in such a way that the graph satisfies the value of x from both the cases.

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

Step by step solution:

The given inequality is

- 2 >|x| - 8

Adding 8 on both sides, we get

- 2 + 8 > |x|

Finally, we get

|x| < 6

We use the definition of , which is

For, x < 0,

We have

Multiplying on both sides, we have

X > - 6

Multiplying on both sides, we have

X > - 6

Or

- 6 < x

For, x ≥ 0,

We have

That is

X < 6

Combining the above two solutions, we get

-6 < x < 6

We plot the above inequality on the real line.

-8 -6 -4 -2 0 2 4 6 8 10

The points -6 and 6 are not included in the graph.

Adding 8 on both sides, we get

Finally, we get

We use the definition of , which is

We have

Multiplying on both sides, we have

Multiplying on both sides, we have

We have

That is

Combining the above two solutions, we get

We plot the above inequality on the real line.

-8 -6 -4 -2 0 2 4 6 8 10

The points -6 and 6 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’.

### Related Questions to study

### Yumiko solved . Explain the error Yumiko made ?

Absolute value of a variable has many uses in mathematics. 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’.

### Yumiko solved . Explain the error Yumiko made ?

Absolute value of a variable has many uses in mathematics. 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’.