Question

Solve the absolute value inequity lx-5l>_ 1

Answer 1

We are given the following the following inequality:

|x - 5| >= 1

When we have a inequality in the format:

|f(x)| >= a

There are two possible solutions.

Either f(x) <= -a or f(x) >= a

In this question:

|x - 5| >= 1

x - 5 <= -1

x <= -1 + 5

x <= 4

Or

x - 5 >= 1

x >= 1 + 5

x >= 6

In interval notation, the answer is:

`(-\infty,4\rbrack\cup\lbrack6,+\infty)`

The solution on the number line is: