Number Properties

[[email protected]]

When is |x-4| = 4-x?

Source: I found this problem in MGMAT number properties example but did not understand the explanation.

[anuprajan5]

Mod (x-4) has 2 values = x-4 and -(x-4)

(x-4) = (4-x)

Therefore mod (x-4) is 4-x when x=4

Regards
Anup

[Anurag@Gurome]

When is |x-4| = 4-x?

Source: I found this problem in MGMAT number properties example but did not understand the explanation.

modulus value is always non-negative.
|x-4| >= 0
so 4 - x >= 0
-> x =< 4
for x =< 4, |x-4| = 4-x

[GMATGuruNY]

For what values of x does |x-4| = 4-x?

4-x is the DIFFERENCE between 4 and x.
A DIFFERENCE can be negative, 0, or positive.

|x-4| is the DISTANCE between x and 4.
A DISTANCE must be greater than or equal to 0.

For the DIFFERENCE between two values to be equal to the DISTANCE between the two values, the DIFFERENCE -- like the DISTANCE -- must be greater than or equal to 0:
4-x ≥0
4 ≥ x.

Thus, |x-4| = 4-x when x≤4.

[[email protected]]

Got it!! I liked the way you made it sound like common sense..

For what values of x does |x-4| = 4-x?

4-x is the DIFFERENCE between 4 and x.
A DIFFERENCE can be negative, 0, or positive.

|x-4| is the DISTANCE between x and 4.
A DISTANCE must be greater than or equal to 0.

For the DIFFERENCE between two values to be equal the DISTANCE between the two values, the DIFFERENCE -- like the DISTANCE -- must be greater than or equal to 0:
4-x ≥0
4 ≥ x.

Thus, |x-4| = 4-x when x≤4.