Question

Rewrite each equation without absolute value
y=|x-3|+|x+2|-|x-5| if x>5

Answer 1

For x>5, the equation without absolute value is y = 3x - 6, obtained by considering the signs of the expressions inside the absolute value brackets based on the condition given.

Step-by-step explanation:

The equation given is y=|x-3|+|x+2|-|x-5| and we are asked to rewrite it without absolute value for x>5.

Since x is greater than 5, we know that:

• x - 3 is positive, so |x-3| = x - 3.
• x + 2 is also positive, so |x+2| = x + 2.
• x - 5 is also positive, so |x-5| = x - 5.

Substituting the values back into the equation, we get:

y = (x - 3) + (x + 2) - (x - 5)

Simplifying, the equation becomes:

y = 3x - 6