... AND you need to be able to recognize IDENTITY and NO SOLUTION problems.
The QUIZ is on sections 3-1 thru 3-4.
pg 190-91 #15-43 ODD, #44-46
OPTIONAL - SUGGESTED HW
pg 193 Mid-Chapter Quiz
What does OPTIONAL - SUGGESTED mean? It means at the very least you need to look at these problems. If they all resemble hw problems that you've done before and you understand them completely, congratulations, you're getting an "A" on the quiz. If you're not sure how to attack a given problem (or two or three), give me a holler on the blog and let's see if we can work it out.
I'll do the suggested homework.. I'll be back if I have any questions :)
ReplyDelete#29 & #31 are both No Solution right..?
ReplyDeleteI don't wanna make any stupid mistakes.
Wait-- For number 33, wouldn't it still be true though, if I ended up with -16<16, because that's true!! But does it have to have the variable in it to be the correct answer?
ReplyDelete*Confuzzled*
In #37, is it supposed to be a fraction..
ReplyDeleteLook at the final "algebraic sentence" after you are done solving for the variable... is it TRUE or NOT TRUE. Then we can discuss.
ReplyDeleteYou (AND EVERYONE) should really do problems #30 and #32, just for a balance of answers.
ReplyDeleteAnd is #39 supposed to be a decimal..? :O
ReplyDeleteCan you even check for No Solution answers?
ReplyDeleteI have a question.. Suppose the answer to a problem was 16>16.. Is that identity? Cuz thats not true.. I know this is what we learned in class but I'm still confused!! Because if it was called Identity, x could = anything to make this true, but its not true!
ReplyDeleteMr. Chamberlain....I wasn't here cuz of king tut...what did we even learn...can you tell me a few of the pages to read.
ReplyDeleteThanks for asking the question, Justin. This message might sound a little harsh or terse... please know that it is intended for EVERYONE in the class, not just you.
ReplyDeleteA message for ANYONE that might be absent on ANY day:
You should be able to check mathchamber.com or this blog and figure out what you missed. If either mathchamber or the blog don't seem up to date, you should email me or call a friend and find out what you missed. As you know, I am "re-building" the website this year based on the new textbook, so I will make every effort to stay at least one step ahead as we move forward through the year.
IF YOU KNOW IN ADVANCE THAT YOU ARE GOING TO BE ABSENT, YOU SHOULD BEGIN THE "CATCHING UP" PROCESS IN ADVANCE, RATHER THAN WAIT UNTIL YOU ARE BEHIND. CALL IT A LIFE SKILL.
Our Algebra text books is organized in a rather straight-forward manner... if you see that the hw is in Section 3.4, you might find it helpful to read section 3.4, ca-peesh? If you email me and wait for an answer, the clock is ticking as you fall behind even further.
The most challenging part of this last homework assignment is the concept of "identity" and "no solution" situations when solving inequalities. So let that be your focus.
WAY BACK ON TUESDAY, WHEN YOU KNEW THAT YOU WERE GOING TO BE ABSENT, you could have arranged some extra help time with me this week. IF YOU CHOSE NOT TO DO THAT, PLEASE UNDERSTAND THE CHOICE WAS YOURS.
All of that said, I am available at lunch time today and, due to a schedule change, I can be available after school as well.
So EVERYONE, do you get the message? This is NOT the math class of the past where you daydreamed during class and did your homework on the bus. THE GAME HAS CHANGED!! PLAY BALL!!
Respectfully,
Mr. C.
i don't understand problem fifteen...don't i need to know the amount of miles from buffalo to st augustine to solve??
ReplyDeletewhen i end up with, for sake, -16<16, would my answer still be true
ReplyDeletefor one of the problems, my answer was 14>=-x...how could 14 be equal to a negative number???
ReplyDeleteI'll take the last question first... when solving equations and inequalities, we are ISOLATING the variable. OUR TARGET IS 'x=' 'x>' 'x>=' (read as x greater than or equal to) 'x<' or 'x<='... got it?
ReplyDeleteSO, if we get -x <= 14 are we at our target yet?
NOOOOOOOOOOOOOOOOOOOOO!!!
How do we get to our target?? We multiply (or divide) both sides by -1, right?
And what happens when we multiply (or divide) by a negative number when solving an inequality (I don't really have to tell you, do I?)
So, the solution is x >= -14
MORE IMPORTANTLY, can '-x' be a positive number?? '-x' is synonymous with 'negative x' which is synonymous with 'the opposite of x'.
Complete this sentence: '-x' is positive when x = ____.
Got it? lmk if this helped!
For #15, you don't need to know anything about the cities or the distance between them or the overall length of the trip. That was extra information designed to make the problem more interesting (or in this case, mislead you!).
ReplyDeleteThe family wants to travel at least 250 miles in 5 hours. How fast do they need to go? Draw a picture. What unit of measure will your answer be? Distance? Time? A rate of distance/time?
Let me know how you make out.
In #29, you probably got ended up at a final step of 9>=9?
ReplyDeleteAsk yourself, is 9>=9. (Answer: Yup!)
SO, regardless of the value of the variable, 9 will always be greater than OR equal to 9 (the keyword being 'OR').
SO, you can answer 'Identity' or 'All real numbers' because if you were to substitute ANY REAL NUMBER for x in this inequality, you would always get a TRUE STATEMENT. Try substituting a few random values for 'x' into this inequality and see what I mean.
In #31, you probably ended up at:
ReplyDelete6 >= -15
... right?
Is that a TRUE STATEMENT?? (Answer: Yup!)
Same explanation as above.
In #33, is -16 < 16 (Yup, again!) getting tired of this yet?
ReplyDeleteFor a different result, try problems 30 and 32.
ReplyDeleteThose answers are NO SOLUTION... see what happens!
Think about it...
ReplyDeleteIf you end up at 16 < 16... is that a TRUE STATEMENT?? (Answer: Nope)
SO, regardless of what number you substitute for 'x' will 16 ever be less than 16? (Nope again).
SO, there is no real number that will ever make this inequality true, therefore: NO SOLUTION is your answer.
Let this be the first entry in your ALGBEBRA TOOLKIT:
ReplyDeleteA solution of an equation or inequality (in one variable) is ANY number that makes the mathematical sentence TRUE.
N.B. The above definition is a combination of the our text book's definition of 'solution of an equation (pg 54) and solution of an inequality (pg165).
SIDEBAR=============================
====================================
Ultimately (NOT YET FOLKS!), we will be working with equations and inequalities in two variables.
On pg 61, the book says:
A solution of an equation with two variables is ANY ordered pair (x,y) that makes the equation true.
Don't worry about that just yet... more misery to come!! (so exciting!!)
Mr. C.
thanks
ReplyDeleteIt would be VERY appropriate for SOMEONE to let me know if my responses have been helpful... otherwise I may find myself inclined not to be so responsive in the future.
ReplyDeleteAnd another thing...
Why am I the only one answering questions? I thought we were a TEAM!!
And another thing...
I'm lookin' at pg193 #1-23 (including the word problems) and I think all of those questions are "FAIR GAME" for the test. Anyone have a problem with that?
BOO!!
Mr. C.
Why when u multiply or divide by a negative number when solving an inequality do u flip the inequality symbol?
ReplyDeleteAs you step through a solution process, each inequality must be EQUIVALENT to the previous INEQUALITY. When you multiply or divide by a negative number, the ONLY WAY to maintain the equivalence, is to reverse the inequality symbol. If you don't do the reversal, you lose equivalence.
ReplyDeleteTake the following inequality:
-3x < 9
Let's solve... divide both sides by -3 and reverse the inequality symbol, and you get:
x > -3
Voila, we solved the inequality. Does our answer check? Let's see. How do we check. We substitute the solution or solutions (in this case there are many solutions, right?).
Well -1 is greater than -3 right?
So, substituting back into the original inequality would yield:
-3(-1) < 9
3 < 9 TRUE!
WHAT IF WE HADN'T REVERSED THE INEQUALITY SYMBOL as a function of the solution process? We would have divided both sides by -3 and had...
x < -3 as our final step, right?
Let's see, -5 is less than -3, right?
So, substituting back into the original inequality would yield:
-3(-5) < 9
15 < 9 FALSE!!
The bottom line is that the solution process WORKS if and only if you reverse the inequality symbol when you multiply or divide both sides by a negative number.