Question

Rewrite each equation without absolute value for the given conditions

y=|x-5|+|x+5| if x>5
y=|x-5|+|x+5| if x<-5
y=|x-5|+|x+5| if -5

Answer 1

If x>5

• Terms are positive

Hence..

• y=x-5+x+5=2x

If x<-5 terms are negative

• y=-x+5-x-5=-2x

If x=-5

• y=|-5-5|+|-5+5|
• y=|-10|
• y=10

Answer 2

Explanation:

Condition 1

x > 5, both terms are positive

• y = x - 5 + x + 5 = 2x

Condition 2

x < - 5, both terms are negative

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

Condition 3

This is not clear