Y=|x-5|+|x+5|, if x>5

Hello,

Let me try out the solution for you.

Consider the below scenarios for the equation y = |x+5|-|x-5|

Case 1:

when x more than or equal to 5

then y = (x+5) - (x-5) = 10

hence y=10

Case 2:

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

y=2x so y can take 9 values corresponding to x={-4,-3,-2,-1,0,1,2,3,4}

Case 3:

when x less than or equal to - 5

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

y=-10

Hence if we combine all 3 cases we get that y can take total of 11 values.

2x

Step-by-step explanation:

y=x-5+x+5

x+x, - 5+5

2x+0=2x

y=2x