Solve each absolute value equation and graph the solution:

The correct answer is: -2 ≤ x ≤ 8

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.
Step by step solution:
The given inequality is
|4x - 12| ≤ 20
We use the definition of |x|, which is

For, 4x - 12 ≤ 0,
We have
|4x - 12| = -(4x - 12) ≤ 20
Multiplying -1 on both sides, we have
4x - 12 ≥ -20
Adding 12 on both sides, we get
4x ≥ -20 + 12
Or
4x ≥ -8
Dividing by 4 throughout, we get
x ≥ -2
For, 4x - 12 ≥ 0,
We have
|4x - 12| = 4x - 12 ≤ 20
Adding 12 on both sides, we have
4x ≤ 20 + 12
Or
4x ≤ 32
Dividing by 4 throughout, we get
x ≤ 8
Combining the above two solutions, we get the solution
-2 ≤ x ≤ 8
We plot the above inequality on the real line.

-3        -2       -1         0         1         2          3         4         5         7          8

Note:
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’.