Question

Y= |x−3| + |x+2| − |x−5|, if x>5 I need to know what y equals.

Answer 1

Answer:

$y \ge9$

Step-by-step explanation:

The given function is

$y = |x - 3| + |x + 2| - |x - 5|$

By the triangle inequality property,

$|x + y| \leqslant |x| + |y|$

and the alternate triangle inequality property;

$|x - y| \geqslant |x| - |y|$

We apply this property to get:

$y \geqslant |x | - |3| + |x | + |2| -( |x | - |5| )$

Expand parenthesis to get:

$y \geqslant |x | - |3| + |x | + |2| - |x | + |5|$

Simplify to get:

$y \geqslant |x | - 3+ |x | + 2- |x | + 5$

Group similar terms to get:

$y \geqslant |x | + |x | - |x | - 3 + 2+ 5$

$y \geqslant |x | + 4$

When x>5,

$y \geqslant |5 | + 4$

That's;

$y \geqslant 5 + 4 \\ y \geqslant 9$