• Problem:
If you add 10 to an integer and then devide the result by -5 the answer you get is -80. What's the integer?
• Solution:
Let's write the equation for the given problem. Adding 10 to an integer can be written as 10 + x in which x is the unknown. Divide the answer by -5 and then equate to -80. We'll have,
[tex] \large \boxed{ \tt \frac{10 + x}{ - 5} = - 80}[/tex]
Let's solve!
[tex] \large \boxed{ \begin{array}{} \tt \frac{10 + x}{ - 5} = - 80 \\ \tt10 + x = - 80( - 5) \\ \tt10 + x = 400 \\ \tt x = 400 - 10 \\ \tt x = 390\end{array}}[/tex]
Thus, the integer is 390.
• To check:
Substitute the value of x to the equation.
[tex] \large \boxed{ \begin{array}{} \tt \frac{10 + x}{ - 5} = - 80 \\ \tt\frac{10 + 390}{ - 5} = - 80 \\ \tt\frac{400}{ - 5} = - 80 \\ \tt - 80 = - 80\end{array}}[/tex]
Therefore, the statement is true and 390 is the correct answer.
