Transcript File

Lesson Topic: Literal Equations &
Inequalities
Ms. Valencia’s Algebra Class
Grade: 8th
10/19/2010
Moving Forward To New & Better
Equations
teacherspayteachers.com, qwickstep.com, green-planet-solar-energy.com, www.mathsteacher.com.au/.../Image1404.gif, prep.math.lsa.umich.edu/pmc/images/8.1.e.5.gif
Prior Knowledge: You should know
that….
 Literal equations
 Contain several letters
 Are formulas
 Inequalities
 Are equations
 Result in a set of numbers which we will use to graph
 Absolute of a negative number is always positive
You should know how to…..
 Literal Equations
 Solve numerical equations
 Solve for the given variable
 Simplify equations
 Inequalities
 Know the difference between <, >, ≤, ≥
 Graph equations
 Find absolute value
What are Literal Equations?
 Literal equations consist primarily of letters .
 FORMULAS.
 Each variable in an equation “literally” represents an
important part expressed by the equation.
 For example: Perimeter of a rectangle
P=2L+2W
What are Inequalities?
 An Inequality is an equation with three differences.
 It is solved just like an equation, except it has NO exact answer.
 It will have many answers that satisfy that inequality.
 We will now use the >, <, ≥, ≤ signs.
 For example: 4+x>1-x; solve for x
In this lesson, you will learn that…..
 Literal Equations
 Equations without constants are solved the same way as
equations with numbers only
 Inequalities
 Are solved just like ordinary equations
 The <, >, ≥, ≤ signs have meanings & play a role when
graphing its solution set
 The solution set determines direction on the number line
 Equations with absolute value will result in two answers
In this lesson, you will learn how to….
 Literal Equations
 Solve literal equations with variables only as well as literal
equations with numbers
 Inequalities
 Solve single, compound, & absolute value inequalities
 Distinguish the meanings between <, >, ≤, ≥ signs
 Graph inequality sets based on its direction
How to Solve Literal Equations?
EXAMPLE 1
F= ab – ap; solve for a
F= a(b – p)
F =
b–p
F =
b–p
F =
b–p
a(b – p)
b–p
a(b – p)
b–p
a
EXAMPLE 2
C= Kh + j; solve for K
h
h*(C= Kh + j)*h
h
Ch= Kh + j
-j
-j
Ch – j= Kh
Ch – j= Kh
h
h
Ch-j= K
h
How to Solve Inequalities?
Single Inequality
6x – 3 < 7 + 4x
6x – 3 < 7 + 4x
+3 +3
6x < 10 + 4x
6x< 10 + 4x
-4x
-4x
2x< 10
2x< 10
2 2
x< 2
Meaning of < ??? Open circle
How to Solve Inequalities?
Compound Inequality
-3 ≤ x – 2 < 4
-3 ≤ x – 2
x–2<4
-3 ≤ x – 2
+2 +2
x–2<4
+2 +2
-1 ≤ x
x<6
-1 ≤ x < 6
Meaning of ≤ and < ??
Closed and open circle
How to Solve Inequalities?
Absolute Value Inequality
10 – 2k ≥ 6
10 – 2k ≥ 6
10 – 2k ≤ -6
10 – 2k ≥ 6
-10
-10
10 –2k ≤ -6
-10
-10
-2k ≥ -4
-2k ≤ -16
-2k ≥ -4
-2
-2
-2k ≤k -16
-2
-2
k≤2
k≥8
k ≤ 2 or k ≥ 8
Worksheet Time
 Activity 1: This worksheet will provide extra practice on
Literal Equations. It is time for your first activity get
prepared to further your learning….YEAH!!!! Let me know
if you need help!!!
Click icon to see worksheet!!
panther.moundsparkacademy.org/.../eqtn-11.gif
Who Is My Partner?
 Activity 3: We are going to play a game that will help you
review <, >, ≤, ≥ signs. The mathematical sign in inequalities
plays a crucial role when it comes to graphing.
 The game will go like so. I will divide the class into two big
groups. One group will have flash cards that will contain
different integers (positive, negative, and absolute value
integers). The other group will have flash cards that contain the
different mathematical signs (<, >, ≤, ≥). Due to the fact that
there are only four signs, the groups will take turns.
Student will say
-31___-27
>
Who is my
Partner?
<
Student
with correct
sign will say
“ I am.’
≤
≥
NO
Sol.
Who Wants To Be A Millionaire
 Activity 2: Students to further your knowledge on Inequalities we
are going to play a FUN game of Who Wants To Be A Millionaire.
The game will consist of various inequality problems. At this
point, please break into your groups of four. Quietly, Thanks.
Are you prepared to WIN A
$1,000,000? Let’s Start..Click on the
number line
algebralab.org
Internet Resources Available
 Extra Help on Literal Equations
WEB PAGE
Click Me
 Extra Help on Inequalities
VIDEO TUTORIALS
Click Here
MINI INEQUALITY GAME
This webpage also contains useful
videos. Take a LOOK.
Click Me
More Practice Problems
Click Here
http://www.youtube.com/watch?v=SKHQFPIOqNk&p=C042AB30BD21BC80&index=1&feature=BF,
http://www.regentsprep.org/regents/math/algebra/AE4/litless.htm , http://www.math-play.com/Inequality-Game.html , sacbee.com
End Of Lesson
 This is the end of our lesson. Now you are experts when it
comes to Solving Literal Equations & Inequalities!
 NOTE: Please let me know if you need extra help…I am here.
Resources
 Algebra 1 Online. (2002-2010). Class work: Solving Inequalities Worksheet. In Module-
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Solving Inequalities. Retrieved October 18, 2010, from
http://teachers.henrico.k12.va.us/math/hcpsalgebra1/module4-1.html
Schultzhie, L. (1998-2010). Literal Equations. In Algebra Lesson Page. Retrieved
October 18, 2010, from
http://www.regentsprep.org/regents/math/algebra/AE4/litless.htm
Ttor68. (2007). A16.15 Inequlity Example. In YouTube. Retrieved October 18, 2010,
from
http://www.youtube.com/watch?v=SKHQFPIOqNk&p=C042AB30BD21BC80&inde
x=1&feature=BF
Popovici, D. (2007). Inequality Game. In Middle School Games. Retrieved October 18,
2010, from http://www.math-play.com/Inequality-Game.html
Valencia, J. How Wants To Be A Millionaire
Brown, R., Dolciani, M., Sorgenfrey, R., Cole, W. (2004). Inequalities CH 10. In
Algebra: Structure and Method- Book 1
Resources Cont..
 Images
 Sacbee.com
 Algebralab.org
 panther.moundsparkacademy.org/.../eqtn-11.gif
 teacherspayteachers.com
 qwickstep.com, green-planet-solar-energy.com
 www.mathsteacher.com.au/.../Image1404.gif
 prep.math.lsa.umich.edu/pmc/images/8.1.e.5.gif
 evanborkowski.com