Question

If I have the following inequality:

-1 <= X <= 1

and Y = 3X

How can I change the inequality to be in terms of Y?

I wasn't sure how to do this, so I just multiplied -1 times 3, and 1 times 3, and replaced X with Y to get:

-3 <= Y <= 3

Now, is this correct?

How would I do this for the same inequality:

-1 <= X <= 1

but when Y = 3-X?

3-(-1) = 4
3-1 = 2

Replacing X with Y and substituting into the new inequality, I get:

4 <= Y <= 2 which does not make any sense.

So what is the method to do this?

Answer 1

-1<= x <= 1

y = 3-x so x = 3-y

-1<= 3-y <= 1 subtract 3 from each

-4<=-y <=-2 change signs and reverse inequalities

4>= y >= 2

check y = 3-x, and when x =1 y = 2, when x = -1, y=4

so y is between 2 and 4 when x is between -1 and 1 QED

Answer 2

@douglaswinslowcooper Thanks. :)

Answer 3

You are very welcome.