Question

# Solve and graph the solution of inequality

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 solve this inequality 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: The points -3 and 3 are not included in the graph. Note:

### Step by step solution:

The given inequality is

|x| < 3

We use the definition of , which is

For, x < 0,

We have

|x| = -x < 3

Multiplying -1 on both sides, we have

x > -3

Or

-3 < x

For

We have

|x| = x < 3

That is

x < 3

Combining the above two solutions, we get

-3< x < 3

We plot the above inequality on the real line.

The points -3 and 3 are not included in the graph.

We use the definition of , which is

We have

Multiplying -1 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.

The points -3 and 3 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’.