Question

Rewrite each equation without absolute value for the given conditions. y = |x−3| + |x+2| − |x−5| if x>5

Answer 1

Using the definition of the absolute value function, it is found that the equation is written as: y = x + 4

What is the definition of the absolute value function?

It is the distance of a given point x to the origin(vertex of the function), hence the definition is as follows:

$|x - a| = x - a, x \geq a$

$|x - a| = -x + a, x < a$

Hence, considering that all expression are positive for x > 5, we have that:

• |x - 3| = x - 3;

• |x + 2| = x + 2;

• |x - 5| = x - 5;

Then, the expression is:

y = |x−3| + |x+2| − |x−5|

y =  x - 3 + x + 2 - x + 5

y = x + 4

More can be learned about the absolute value function at https://brainly.com/question/24734454