# The sum of two and the quotient of a number and eight is negative seven. What is the number?

Dec 15, 2016

Call the number $x$ and break up the problem

#### Explanation:

"quotient of a number and eight" $= \frac{x}{8}$

"the sum of two and ..." $= 2 + \frac{x}{8}$

"is negative seven" $2 + \frac{x}{8} = - 7$

Now we have something we can work with:
Subtract $2$ from both sides:

$\cancel{2} - \cancel{2} + \frac{x}{8} = - 7 - 2 \to \frac{x}{8} = - 9$

Multiply both sides by $8$:

$\cancel{8} \times \frac{x}{\cancel{8}} = - 9 \times 8 \to x = - 72$

$2 + \frac{- 72}{8} = 2 - 9 = - 7$ Check!