i don't understand
write an equation to
solve the following. show all your work, including the steps for
solving the equation and checking your answer.
–4 times a
number plus 16 is –116. find the number.

-4(x)+16= -116

You need to figure out what 'x' equals. 
To find that you need to do the problem (more or less) backwards. 

 -116 - 16 

You have to subtract '16' from '- 116'

-116 - 16 = -132

-132 / -4

Then you divide '-132' by '-4'

-132 / -4 = 33

x= 33

The problem would look like this:

-4(33)+16= -116

~The parenthesis around the '33' just mean you multiply it~