Are YOU READY for the QUIZ?? You can ask your questions here!! And you can answer your buddies questions, too, ya know... I'm tired of doing EVERYTHING around here!!
I'm hoping a generic response will answer your specific question.
If you use an algebraic property that will CHANGE/TRANSFORM values, then you must change ALL VALUES in the same way. That is just a fancy way of re-stating the Cardinal Rule of solving equations, which is: "(DUH!) Whatever you DO to one side of an eqaution, you MUST DO to the other."
You want to get rid of that UGLY FRACTIONAL COEFFICIENT, don't you? Hey, fractions have feelings, too, ya know... you don't have to be so mean about it! (jk)
Seriously, as you recognized the best to attack a fraction, or group of fractions, (aka FRAC-ATTACK!) is to multiply by the least common denominator. In this case, there is only one denominator, namely 5. So multiplication by 5 (across the board, of course) does the trick.
Again, if we learn to ask the SAME QUESTIONS every time, all problems (and SOLUTIONS!) start to look and sound much more similar as well.
It's kind of like this one-act play between Charmi and the math gods:
Math gods(echoing from the clouds): "What don't we like about this equation, Charmi?" Charmi(glancing suspiciously upward): "Well, almighty math gods, we don't like the fractional coefficient, of course." Math gods(louder, more forceful): "What is the denominator of "5" doing here, Charmi??" Charmi (quivering): "It is acting as a DIVISOR, oh great ones!" Math gods(in a booming voice): "Well then, how do we attack DIVISORS?" Charmi(cowering, near tears): "With multiplication, of course." Math gods(thunder, lightning, volcanoes erupting): And since there are two terms on the left side of this equation (PS 3A #11), what PROPERTY do we need to INVOKE??!!" Charmi(rain-drenched, on knees, pleading for mercy, shouting yet barely audible through the wind and rain):We have to use the DISTRIBUTIVE PROPERTY, oh vaunted ones!!" Math gods(in a soothing voice, sun is now shining):"That's right, Charmi. Well done. Aren't you glad you asked?" Charmi(relieved, wringing out her sweater):"Oh yes, math gods, thank you so much for your help. I don't think I have any more questions right now." Math gods(birds chirping gleefully in the background):"That's wonderful, Charmi. Enjoy the rest of your day, and stop by anytime for more help." Charmi(with fingers and toes crossed);"Oh yes, almighty math gods, I will be back soon!"
Then, suddenly from behind a rock, Schlmozzl, the orphan math god whispered to Charmi:
"Actually, you could have subtracted 4 from both sides and avoided the whole distribution property thing. Then, you could have ditched the fractional coefficient by multiplying BOTH SIDES by the reciprocal, which in this case is (-5/2). There's always more than one way to solve an equation. I think my way is better. Mum is the word with the math gods, they thought they got rid of me long ago, in the Variable Volcano Eruption of 1991. Bye for now."
Yup 18-2x and -2x+18 are equivalent expressions. We will learn later in the year, that algebraic expressions should be written in "descending order of degree" of the exponents, e.g.
2x^2 + 3x - 5 is in proper order 3x - 5 + 2x^2 is not in proper order
on number three i got 2x+10. the steps on the answer jey are confusing. What did I do wrong? this is my work: 4-2[x-7] 4-2x-14 dist. prop 2x-4-14 commutative property 2x-[-10] combine like terms 2x+10 simplify
This Blog exists for the collective benefit of all algebra students. All questions are welcome. The more specific your question (including your own attempts to answer it) the better.
EVEN MORE WELCOME ARE ANSWERS FROM FELLOW STUDENTS. BLOG ON!
hiya!!!! m,y question is for question 11 you have to mulitiply -5 to the 4 the -5 ND THE 8 RIGHT?
ReplyDeletefor the next test, diamond problems won't be on them right?
ReplyDeletehmmm... I would think EVERYONE would WANT diamond problems to be on the next test. Who doesn't LOVE diamond problems??
ReplyDeleteHi Charmi,
ReplyDeleteI'm hoping a generic response will answer your specific question.
If you use an algebraic property that will CHANGE/TRANSFORM values, then you must change ALL VALUES in the same way. That is just a fancy way of re-stating the Cardinal Rule of solving equations, which is: "(DUH!) Whatever you DO to one side of an eqaution, you MUST DO to the other."
You want to get rid of that UGLY FRACTIONAL COEFFICIENT, don't you? Hey, fractions have feelings, too, ya know... you don't have to be so mean about it! (jk)
Seriously, as you recognized the best to attack a fraction, or group of fractions, (aka FRAC-ATTACK!) is to multiply by the least common denominator. In this case, there is only one denominator, namely 5. So multiplication by 5 (across the board, of course) does the trick.
Again, if we learn to ask the SAME QUESTIONS every time, all problems (and SOLUTIONS!) start to look and sound much more similar as well.
It's kind of like this one-act play between Charmi and the math gods:
Math gods(echoing from the clouds): "What don't we like about this equation, Charmi?"
Charmi(glancing suspiciously upward): "Well, almighty math gods, we don't like the fractional coefficient, of course."
Math gods(louder, more forceful): "What is the denominator of "5" doing here, Charmi??"
Charmi (quivering): "It is acting as a DIVISOR, oh great ones!"
Math gods(in a booming voice): "Well then, how do we attack DIVISORS?"
Charmi(cowering, near tears): "With multiplication, of course."
Math gods(thunder, lightning, volcanoes erupting): And since there are two terms on the left side of this equation (PS 3A #11), what PROPERTY do we need to INVOKE??!!"
Charmi(rain-drenched, on knees, pleading for mercy, shouting yet barely audible through the wind and rain):We have to use the DISTRIBUTIVE PROPERTY, oh vaunted ones!!"
Math gods(in a soothing voice, sun is now shining):"That's right, Charmi. Well done. Aren't you glad you asked?"
Charmi(relieved, wringing out her sweater):"Oh yes, math gods, thank you so much for your help. I don't think I have any more questions right now."
Math gods(birds chirping gleefully in the background):"That's wonderful, Charmi. Enjoy the rest of your day, and stop by anytime for more help."
Charmi(with fingers and toes crossed);"Oh yes, almighty math gods, I will be back soon!"
The End
Then, suddenly from behind a rock, Schlmozzl, the orphan math god whispered to Charmi:
ReplyDelete"Actually, you could have subtracted 4 from both sides and avoided the whole distribution property thing. Then, you could have ditched the fractional coefficient by multiplying BOTH SIDES by the reciprocal, which in this case is (-5/2). There's always more than one way to solve an equation. I think my way is better. Mum is the word with the math gods, they thought they got rid of me long ago, in the Variable Volcano Eruption of 1991. Bye for now."
(to be continued...)
hahahahahha okay? :)
ReplyDeleteum..........is Schlmozzl the blue math god? with the yellow or is that the opposite?
ReplyDeletehahahaha thanks for answering my question-in SUCH detail
for number 3 in the packet- i it okay i if write 18-2x not -2x+18? i mean itb is the same thing right?
ReplyDeleteYup 18-2x and -2x+18 are equivalent expressions. We will learn later in the year, that algebraic expressions should be written in "descending order of degree" of the exponents, e.g.
ReplyDelete2x^2 + 3x - 5 is in proper order
3x - 5 + 2x^2 is not in proper order
... but for now, I will accept either.
Mr. C.
P.S. Schlmozzl is invisible
on number three i got 2x+10. the steps on the answer jey are confusing. What did I do wrong?
ReplyDeletethis is my work:
4-2[x-7]
4-2x-14 dist. prop
2x-4-14 commutative property
2x-[-10] combine like terms
2x+10 simplify
nevermind i see now =]
ReplyDeleteanother way to look at that problem is to re-write (or "Simplify - add the opposite") before you distribute:
ReplyDelete4 - 2(x - 7)
4 - 2[x + (-7)]
When you re-write it this way, it may be more clear that you are removing 2 sets/groups of 7 negatives... ca-peesh??
Mr. C.
What are we supposed to do for the algebra toolkit definitions? I couldn't find anything explaining it on mathchamber.
ReplyDeletei agree with kate......:)
ReplyDelete