Solve and graph the inequality: |x| < 3.
The inequality |x| < 3 can be written as
-3 < x < 3
To draw the graph of the inequality consider all points of x that lie between -3 and +3 but do not include -3 and +3.
This gives all the value that x can take as those that lie in the set (-3 , 3).
To solve the inequality, we'll have to apply the definition of the absolute value:
|x|<c <=> -c<x<c
For c = 3 => -3 < x < 3
We'll solve the simultaneous inequalities:
-3 < x and x < 3
-3 < x <=> x belongs to the range (-3 ; +infinite)
x < 3 <=> x belongs to the range (-infinite ; 3)
We'll intercept the intervals and the common solution for x is found in the opened interval (-3 ; 3).