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’.
