how do you solve -4(x-3) is greater than -4 and what is the answer?

Almost Saseflower,  When you multiply or divide by a negative number you have to turn the sign around.

Lok at this

12>8    true....yes

divide by -4

12/-4>8/-4

-3>-2     is that true ?   NO it is not - you have to turn the sign around.

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You also have to swap the sign around if you swap side     

eg    6>8

but   8<6

And lastly,  You also have to swap the sign if you take the reciprocal of both sides

ex      $$\frac{6}{5} <2$$

but    $$\frac{5}{6} > \frac{1}{2}$$

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Other than the sign swap your answer was fabulous.  Fix it up (by editing) and I will give you 3 more points :)

-4 (x - 3) > -4

Use distributive property

-4x - (-12) > -4

Simplify (you can skip this step and instead put the equation that is below, up ^ if that makes sense)

-4x + 12 > -4

Subtract 12 from both sides

-4x > -16

Divide by -4 on both sides

x > 4

And there's your answer :)