Answer:
We know that the function IxI is such that:
IxI = x if x ≥ 0
IxI = -x if x < 0.
In this case, we have:
A = I3x - 6I + 2
If we do the same as above, we can write:
A = (3x - 6) + 2 if (3x - 6) ≥ 0
Let's look at the condition in the right, let's isolate the variable:
(3x - 6) ≥ 0
3x ≥ 6
x ≥ 6/3 = 2
Then the condition:
(3x - 6) ≥ 0
is equivalent to:
x ≥ 2
Then we can write:
A = (3x - 6) + 2 if x ≥ 2
If we simplify it further, we get:
A = 3x - 6 + 2 if x ≥ 2
A = 3x - 4 if x ≥ 2
This is what we wanted to prove.
