Video Transcript
Find the solution set of the
inequality the absolute value of 𝑥 minus six is greater than or equal to seven.
In order to solve any absolute
value problem of this type, we need to solve two inequalities. This is because the absolute value
of a number is its distance from zero. In this question, we want the
distance to be greater than or equal to seven. Firstly, the value inside our
absolute value, 𝑥 minus six, could be greater than or equal to seven. Alternatively, 𝑥 minus six could
be less than or equal to negative seven. Adding six to both sides of our
first inequality gives us 𝑥 is greater than or equal to 13, and adding six to both
sides of our second inequality gives us 𝑥 is less than or equal to negative
one.
We can demonstrate this on a number
line. As 𝑥 is greater than or equal to
13, we have a closed circle at 13 and 𝑥 can take any value to the right of
this. Likewise, as 𝑥 is less than or
equal to negative one, 𝑥 can take any value including and to the left of this
value.
This means that the solution set
contains all real values apart from those between negative one and 13. This can be written as the real
values minus the open interval from negative one to 13.
