how to solve two step equations?

-9x + 1 = -80
-9x = -80 - 1
-9x = -81
x = -81/-9
x = 81/9
x = 9

- 9x + 1 = - 80
9x = 80 + 1
9x = 81
x = 9

Answer: x = 9

Proof:
- 9(9) + 1 = - 80
- 81 + 1 = - 80

- 9 x = - 81
9x = 81
x = 9

since 1 is annoying to do the problem with, subtract it (since its a positive 1) on both sides of the equal sign. then, to get x by itself, divide both sides by -9. -81/ -9 is 9. (just remember that what you do to one side, you have to do to the other too) so, x=9

Basically, what you do, as everyone has been trying to demonstrate, is you make sure that you perform operations that keep both sides equal, by doing the same thing to both sides each step of the way. If you do that, then the 'truth' of the equation is preserved. So, step by step (well, not EXACTLY step by step...even with this many, I'm taking short cuts).

-9x + 1 = -80
[means]
(-9*x) + 1 = -80
[+ (-1) to both sides]
(-9*x) + 1 + (- 1) = -80 + (-1)
[means]
(-9*x) + (1-1) = -(80+1)
[means]
(-9*x) + (0) = -(81)
[means]
-9*x = -81
[divide both sides by -9]
-9*x/-9 = -81/-9
-9/-9 * x = 9
1 * x = 9
x = 9

Equation is solved for x. Now, if this were a logical proof, you'd have to justify each step you took, and take more steps to justify each change by only one 'rule' or axiom.... but, really, practically, most, if not all, of the other solutions are all you need for most teachers to 'see your work'.

-9x+1=-80
-1 -1
-81
you subtract 1 on both sides so you can divide

-9x=-80
divide both sides by 9
-x=-9
since both 9 and x are negative you can make them postive
x=9

-9x+1=-80
Multiplying through out by -
-(-9x+1)=-(-80)
9x-1=80
9x=81
x=81/9
x=9

-9x+1=-80

put like terms on either side of the equation, by adding the same amount to each side

-9x+1 + (-1)=-80 + (-1)
-9x=-81

multiply each side of the equation by the same amount

-9x * (-1/9) = -81 * (-1/9)
x = 9

-9x+1=-80
thus
9x = 81
divide both sides by 9
x = 9

Check
-9(9) +1=-80
-81 + 1 = -80
-80 = -80

-9x+1=80
-1 -1
-9x=79(divide both sides by -9)
-8.77777 or -8.8