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 27.5, 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.