Question

A=|3x-6| + 2 , xeR
prove that:
A=3x-4 for every x≥2​

Answer 1

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.