INT MATHGet into your ORIGINAL groups with the helper
(will switch later)
Copy and complete.
SIMPLIFY the following Rational Expressions
Inequalities: REVIEW NOTES
(chapter 6 in red book)
WHAT you KNOW (only has ONE variable):
1. Solve them like regular problems (for the variable)
2. DIVIDE or MULTIPLY by a negative you FLIP the sign
3. GRAPH on a NUMBER LINE
4. VAriable solved and on the LEFT then the ineqiality sign
POINTS in the direction to be shaded
5. <
> are OPEN circles,
<
>
are closed circles
EXAMPLE:
GREAT let's make sure we are all on the same page....
USE the leader in your group.
DO these 2 problems--CHECK ANSWER with each other
NO SIDE CONVOS-- we are moving fast
HOW do you check your answer?
COMPUND Inequalities:
LOOK LIKE: 2 inequality signs in problem
"AND" ones look like one long prob
"OR" ones look like 2 sep. ones
1. Break into 2 problems
2. SOLVE each inequality separatley
(RULES for regular inequ. still apply)
3. Bring back together IF you can
4. GRAPH BOTH on SAME number lines
5. "AND" the graph SHOULD overlap
"OR" the graph SHOULD go in oppostie directions
Examples: REMEBER you know this--it is just
MORE steps in the SAME problem
ADDENDUM to inequalites......
SAY you solve it correct.....YOU KNOW this cause you
have confidence
There are problems whose Answers are
"no solution"
"all real numbers"
WATCH: pg. 291 # 3c, #6
Absloute Value Linear Inequalites
LOOKS like: has ONE inequality sign, has
ABS signs
1. RE-WRITE problem as 2 cases (CHECK to see if you have
to simpplify FIRST before you do this)
**drop off ABS signs
**CASE 2 --CHANGE stuff on right side to NEG
AND FLIP the inequality sign
2. SOLVE each one like regular Sepearatly
3. Graph like you would a compund one if possible
4. MENTALLY- sub in numbers to check to see if they fir
nd your graph matches
EXAMPLE: Solving absolute value inequalities
SOLVING absolute value inequalites with other JUNK
**get rid of the other stuff FIRST before you split
into 2 cases.
ADDENDUM:
Absloute Value equations (do same steps)
(2 answers- just when you graph them they are
dots and no shading)
ADDENDUM # 2 to ABS equations and inequalites
Some will "TRICK" you....
Think......
Are these possible?????
AWESOME:
Let's see how you roll......
SUMMARY:
*divide/multiply by neg- FLIP SIGN
COMPOUND INEQUALITIES:
*"AND"- 2 answers graph should overlap (break into 2
problems)
*"OR"- 2 answers graph should go opposite ways
ABSOLUTE VALUE INEQUALITES:
*break into 2 cases (2nd case- change right to neg and flip
sign)
You got ALL this..... or can if you practice on your own???
Complete pg. 310 # 1-35 odd, pg. 312 # 61 to 71 odd
(covers all types)