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

Your value is any rational number greater than 27.527.5, or 55/2552.

Explanation:

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

-8x > -2208x>220

(-8x) / (-10 + 2) = x8x10+2=x

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

(-8x) / (-10 + 2) = x8x10+2=x

(-8x)/-8 = x8x8=x

x = xx=x

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

Now to work out the inequality:

-8x > -2208x>220

x < 27.5x<27.5

So, the value of xx is any rational number greater than 27.527.5, or 55/2552.