Bunuel wrote:
nkimidi7y wrote:
When is |x-4| = 4-x?
A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0
I could answer this question by plugging in some numbers.
But how do i prove this using algebra?
Absolute value properties:When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);
When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);
So, \(|x-4|=4-x=-(x-4)\) to be true should be that \(x-4\leq{0}\) --> \(x\leq{4}\).
Answer: D.
Hope it's clear.
I am still new to modulus so please do bare with me if I sound stupid.
This problem can be solved easily by picking numbers but to understand the concepts I tried to solve it using the books I read.
So according to the book, I need to take into account when the modulus is positive and negative when solving
\(x-4>0, x>4\)
x-4=4-x
x=4
(not sure if this value has to be rejected or not. Please help)
and when \(x+4<0, x<=4\)
-(x+4)=4-x
-x-4=4-x
Just lost here.
My question is why do we chose X<=4 why do we chose one condition over the other.