Question

Set up the equation for the following word problem and solve the equation. Let z be the unknown number. −83 times a number minus 71 is equal to −91 less than the number.write out the equation

Answer 1

z is the unknown number

-83 times a number means: -83z

This result minus 71 means: -83z - 71

This result is equal to means: -83z - 71 =

-91 less than the number means: z - (-91)

Then the equation is:

$\begin{gathered} -83z-71=z-(-91) \\ -83z-71=z+91 \end{gathered}$

To solve the equation, follow the next steps:

$\begin{gathered} \text{Subtract z from both sides} \\ -83z-71-z=z+91-z \\ -84z-71=91 \\ \text{Add 71 to both sides} \\ -84z-71+71=91+71 \\ -84z=162 \\ \text{Divide both sides by -84} \\ \frac{-84z}{-84}=\frac{162}{-84} \\ z=-\frac{162}{84} \\ \text{Simplify} \\ z=-\frac{27}{14} \end{gathered}$