Interpreting "x = |y - z|"

Question

Hello,

In a DS question like " Is |x-3| = 4?", we can translate the stem into "Is the distance of x from 3 on a number line equal to 4?".

In similar lines, what is meant by the following question stem?
 Is x = |y - z| ?

Thanks,
dshailen

EvaJager · Answer

|x - 3| = 4 also means that x - 3 = 4 or x - 3 = -4, so x can be either 7 or -1. On the number line, it means go a distance of 4 to the left of 3 - you will find -1, or go a distance of 4 to the right of 3 - you will find 7.

Algebraically, |x| = x if x is non-negative, and |x| = - x if x is negative. |7| = 7 and |-7| = -(-7).
|y - z| means the distance between y and z and this distance must be x. |y - z| = y - z if y > z, and |y - z| = z - y if y < z.
It is easier now to use the algebraic approach. In order to express a distance, x must be non-negative.
Then, |y - z| = x if y - z = x or y - z = - x.

KarishmaB · Answer

|y - z| represents the distance between y and z on the number line. 
|y - z| = |z - y| It still remains the distance between the two points on the number line.

When you say x = |y - z|, you are saying that x is the distance between y and z on the number line. This implies that x cannot be negative.

This is parallel to the first example you used: |x-3| = 4 
The distance of x from 3 (or distance of 3 from x i.e. distance between x and 3) is 4.

Interpreting "x = |y - z|"

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