Algebra question

[Scuff]

4 - 2x =g

-2x=g - 4

X = (4 - g) / 2

 

Help me out here; it's been a few years. ;) How does the negative distribute when you move the 2 over? Why is the 2 positive, but everything on top opposite? Would it also be correct to say x = (g - 4) / -2?

[Cosmos]

4 - 2x =g

-2x=g - 4

X = (4 - g) / 2

 

Help me out here; it's been a few years. ;) How does the negative distribute when you move the 2 over? Why is the 2 positive, but everything on top opposite? Would it also be correct to say x = (g - 4) / -2?

 

Yes, but it would not be simplified.

 

A fraction with a negative denominator is not considered simplified. So the negative could be applied to the entire fraction:

 

                 g   -   4

x   =     -   ----------

                      2

 

 

Even better, distribute the negative through the numerator:

 

                 -g   +   4

x   =          ----------

                      2

 

 

That one is not wrong, but most mathematicians prefer not to lead with a negative term, so this would be better:

 

                 4   -   g

x   =         ----------

                      2

 

 

These display fine on my screen. I'm hoping it works for others as well.

[Scuff]

Thank you!

[kiana]

Related to the excellent explanation above, being able to move smoothly between -(g-4) and 4-g is something that people tend to struggle with in my lower-division classes at the college. It is a subskill worth practicing if your student struggles with it.