When you take my value and multiply it by -8, the result is an integer greater than -220. If you take the result and divide it by the sum of -10 and 2, the result is my value. I am a rational number. What is my number?

1 Answer
Jan 11, 2018

Answer:

Your value is any rational number greater than #27.5#, or #55/2#.

Explanation:

We can model these two requirements with an inequality and an equation. Let #x# be our value.

#-8x > -220#

#(-8x) / (-10 + 2) = x#

We will first attempt to find the value of #x# in the second equation.

#(-8x) / (-10 + 2) = x#

#(-8x)/-8 = x#

#x = x#

This means that regardless of the initial value of #x#, the second equation will always be true.

Now to work out the inequality:

#-8x > -220#

#x < 27.5#

So, the value of #x# is any rational number greater than #27.5#, or #55/2#.