# 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?

Jan 11, 2018

Your value is any rational number greater than $27.5$, or $\frac{55}{2}$.

#### Explanation:

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

$- 8 x > - 220$

$\frac{- 8 x}{- 10 + 2} = x$

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

$\frac{- 8 x}{- 10 + 2} = x$

$\frac{- 8 x}{-} 8 = x$

$x = x$

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

Now to work out the inequality:

$- 8 x > - 220$

$x < 27.5$

So, the value of $x$ is any rational number greater than $27.5$, or $\frac{55}{2}$.