Ms. Valencia’s Algebra ClassGrade: 8th 10/19/2010

Lesson Topic: Literal Equations & Inequalities

Moving Forward To New & Better Equations

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Prior Knowledge: You should know that….

You should know how to…..Literal Equations

Solve numerical equationsSolve for the given variableSimplify equations

InequalitiesKnow the difference between <, >, ≤, ≥Graph equationsFind 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 EquationsEquations without constants are solved the same

way as equations with numbers onlyInequalities

Are solved just like ordinary equationsThe <, >, ≥, ≤ signs have meanings & play a role

when graphing its solution setThe solution set determines direction on the number

lineEquations with absolute value will result in two

answers

In this lesson, you will learn how to….

Literal EquationsSolve literal equations with variables only as well

as literal equations with numbersInequalities

Solve single, compound, & absolute value inequalities

Distinguish the meanings between <, >, ≤, ≥ signsGraph inequality sets based on its direction

How to Solve Literal Equations?

EXAMPLE 1F= ab – ap; solve for a

F= a(b – p)

F = a(b – p)b – p b – p

F = a(b – p)b – p b – p

F = ab – p

EXAMPLE 2C= 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 Inequality6x – 3 < 7 + 4x

6x – 3 < 7 + 4x +3 +3

6x < 10 + 4x

6x< 10 + 4x-4x -4x

2x< 10

2x< 1022

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 x – 2 < 4+2 +2 +2 +2

-1 ≤ x x < 6

-1 ≤ x < 6

Meaning of ≤ and < ??Closed and open circle

How to Solve Inequalities?Absolute Value Inequality10 – 2k ≥ 6

10 – 2k ≥ 6 10 – 2k ≤ -6

10 – 2k ≥ 6 10 –2k ≤ -6 -10 -10 -10 -10

-2k ≥ -4 -2k ≤ -16

-2k ≥ -4 -2k ≤ -16-2 -2 -2 -2

k ≤ 2 k ≥ 8

k ≤ 2 or k ≥ 8

k

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.

-31___-27 Who is

my Partner?

> ≤

≥<

Student will say 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

Extra Help on Inequalities

VIDEO TUTORIALSClick Here

WEB PAGE Click Me

MINI INEQUALITY GAMEThis webpage also

contains useful videos. Take a LOOK.

Click Me

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

More Practice ProblemsClick Here

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- 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&index=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.comAlgebralab.orgpanther.moundsparkacademy.org/.../eqtn-11.gifteacherspayteachers.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.gifevanborkowski.com