Simplify the expression for the given values of $$ x $$. $$ |x-1|-|x-2| $$ if $$ x \geq 4 $$ Answer:

Question

UpStudy AI · Accepted Answer

Given the expression

$$
|x-1| - |x-2|
$$

and knowing that $$ x \geq 4 $$, we analyze each absolute value term.

1. For $$ x \geq 4 $$, the expression $$ x-1 $$ is non-negative because $$ x-1 \geq 3 $$. Thus, we have:
   $$
   |x-1| = x-1.
   $$

2. Similarly, for $$ x \geq 4 $$, the expression $$ x-2 $$ is also non-negative because $$ x-2 \geq 2 $$. Thus, we have:
   $$
   |x-2| = x-2.
   $$

Substitute these back into the original expression:

$$
|x-1| - |x-2| = (x-1) - (x-2).
$$

Simplify the expression:

$$
(x-1) - (x-2) = x - 1 - x + 2.
$$

Combine like terms:

$$
x - x - 1 + 2 = 1.
$$

Thus, for $$ x \geq 4 $$,

$$
|x-1| - |x-2| = 1.
$$
For $$ x \geq 4 $$, the expression simplifies to 1.

Simplify the expression for the given values of \( x \). \( |x-1|-|x-2| \) if \( x \geq 4 \) Answer: