The first thing you should know is about the modulus
function. The modulus makes any function within it
positive. Here's a few simple examples
to show you that:
|3| = |-3|
|-100| = |100|
|x - 2| = |2 - x|
|10x - 3| = |3 - 10x| and so on.
Hence you can conclude the result that in
general, |x - y| = |y - x|.
Now, the first pattern that you should notice is that |2x - 5|
is a factor of |10 - 4x|.
|10 - 4x| = 2 |5 -
2x|
(Factorise out a positive 2)
Heading over to the question,
|2x - 5| + 2|10 - 4x| = 15
|2x - 5| + 4|5 - 2x| = 15
From the previous result that we have derived, we can conclude
that |2x - 5| = |5 - 2x|
To make things easier to see, we let y = |2x - 5| = |5 - 2x|
y + 4y = 15
y = 3
Therefore, |2x - 5| = 3
=> 2x - 5 =
3
or
-2x + 5 = 3
Hence x = 4 or x =
1.