Algebra 26 - Solving Literal Equations

[@MyWhyU]

Freddie Frillman: Only numbers which are common factors of both the numerator and denominator can be canceled. In your example (p - 2w)/2, two is not a factor of the numerator since it is not a common factor in every term added together to create the numerator, i.e., it is a factor of 2w but not p. On the other hand, in (4p-2w)/2, two is a common factor of both the numerator and denominator since the two terms in the numerator 4p and -2w, both contain a factor of two. Therefore (4p-2w)/2 = 2(2p-w)/2 = 2p-w.

[@FreddieF]

Oh... ok. Thank you!

[@jdpazmino2010]

This is great! The explanations are brief but do a good job of relating the equation to the real world, LOGICALLY. Teachers stumble over this often.

[@OMARYassin1]

very great information .. very great way to introduce it .. Keep up you're great

[@benjaminpetrofsky819]

I have a question, can someone help? At 7:00, we need the reciprocal of a, but a is still in the denominator. I thought you switch reciprocals? Any help would be great.

[@ashaydwivedi420]

@Benjamin Petrofsky, if we reciprocate any number "a", it will be "1/a". "a" will always be in the denominator

[@FreddieF]

Wait!! In the equation (p - 2w)/2 = l, can't you just write the fraction on the left as (p - w)? Because the two in the denominator cancels the 2 multiplier of w in the numerator... right?

[@kaizenwichy]

In the last step of solving n for: npq+rt=nz, (time is 11:10) you multiplied the right member of the equation by -1 to make the numerator positive, but you didn't multiply the literal on the left side of the equation by the same "-1". Is it possible to multiply only one side of the equation by -1?

[@MyWhyU]

Since the numerator and denominator in the fraction on the right side of the equation were both multiplied by -1, this was the same as multiplying by -1/-1 = 1 so the left side did not have to be multiplied by -1.

[@kaizenwichy]

Ok, My understanding was that the same operation needed to be performed on both sides of the equation (multiplying both sides by -1 would yield "-n" on the left side of the question). Thanks

[@MyWhyU]

You are correct that if one side of an equation is multiplied by a constant, then the other side must be multiplied by the same constant in order to keep the two sides equal. However, multiplying the numerator and denominator of a fraction by the same number (in this case -1) does not change the value of that fraction. SInce the right side of the equation has not been changed, the equation is still valid.

[@torosalvajebcn]

The explanation by the Professor is gret and very technical. I also doubted at that point but then I had an instictive solution. In a división, if both numerator and demominator are positive, or ngative, changing both their signs to negative or positive will give the same positive result. If they are different, changing their signs will give the same negative result, so it really doesnt affect the term on the left.

[@AngeloGi]

Can't wait 'till we get into Calculus! (We will...right?)

[@MyWhyU]

After Algebra we will delve into the amazing realm of Calculus.

[@AngeloGi]

Yes!

[@nawafddi]

***** Calculus! thank you so much

[@FreddieF]

The last two episodes were uploaded in fast succession.

[@pauldow1648]

Thank you