Equiations and inequalities

EQUATIONS AND INEQUALITIES

IN ONE VARIABLE

By : Mr Ronald Naradus SSMPK PENABUR GADING SERPONG

EQUATIONS AND INEQUALITIES IN ONE VARIABLE

Mathematics Sentence Equations

Statement

Open Sentence

Solving Equation

Properties

Equation

DefinitionClosed Sentence

Inequalities

Definition

PropertiesInequalitie

s

Solving Inequaliti

es

Glossary

Open sentence = kalimat terbuka

Closed sentence = kalimat tertutup

Open mathematical sentence = kalimat matematika terbuka

Equation = persamaan

Side = ruas

Member = suku, bagian

Equation of one variable = persamaan satu peubah

Linear equation of one variable = persamaan linear satu variabel

First-degree equation, equation of degree one = persamaan berderajat satu

Solution of the equation = penyelesaian persamaan

Solution set = himpunan penyelesaian

Equivalent equations = persamaan yang ekuivalen

Inequality = pertidaksamaan

Inequality of one variable = pertidaksamaan satu variabel

Linear inequality of one variable = pertidaksamaan linier satu variabel

Interval = interval, selang

STATEMENTS

1. The prime numbers are always odd number

2. Stanley is a great student

What is the different between both sentence?

Statement means any sentences that can be determined for its value of truth ( either true or false ) but not both values

Statements

State weather the following are true or false !

a. The number of players in a football team is 12.

b. 2 is not prime numberc. 21+15 35d. -20 -19e. A negative number plus a negative number

is a positive numberf. Medan is capital of west sumatera province g. The sun arises from westh. 2 + 3 = 6

FF

TF

FF

FF

The following are not examples of statements

a. Have you learnt mathematics ?b. Study hardc. Durian’s taste is very deliciousd. Trader is rich persone. The girl is very attractive

*Open sentence

Is the sentence “ y is a person who was Indonesian president “ true or false ?

If y replaced by Ir. Soekarno, then the sentence becomes a statement having

true value

While if y is replaced by Hitler, then the sentece becomes an a statement having

false value

Then, Ir soekarno is solution for its statement

Or

y = Ir soekarno

An open sentence is a sentence which cannot be determined whether it is a correct or incorrect sentence.

A closed sentence is a correct or incorrect sentence.

EXAMPLE

o☺minus to 33 equal to 11 ( open sentence )

o☺= 44 ( solution )

o44 minus to 33 equal to 11( Closed sentence )

DO EXERCISE 32PAGE 49 NO. 1 - 3

APPLICATION OF LINEAR EQUATION IN DAILY LIFE

the following are several terms commonly used in narrative problem and how to write them.

NO Terms How to Write

1 The sum of m and n m + n

2 The difference between m and n, m > n m – n

3 The sum of the square of m and n m2 + n2

4 The square of the sum of m and n (m + n)2

5 The difference between the square of m and n, m > n m2 – n2

6 The squared of of the difference of m and n , m > n (m – n )2

7 The opposite of m -m

8 The reciprocal of m

9 The sum of reciprocal of m and n

10 The reciprocal of the sum of m and n

11 The product of m and n mn

Equation is an open mathematical sentence which contains an equality sign “ = “

Equations

A linear equation in the variable x is an equation that can be written in the form

ax + b = 0 where a is coefficients, b is constants and a ≠ 0.

A linear equation is also called a first-degree equation or an equation of

degree one.

3x − 7 = 0 and 5x = 25 are linear equations.

Linear Equations

Solving an Equation

Three Operations

How do we solve equations with inverse operations?

• Let’s take a look at a simple equation

Step 1:- 13

Answer:

2113 x- 13

8x

Now that we have solved the equation, let’s check the solution:

2121

2113 x21138

HOW DO WE SOLVE EQUATIONS WITH INVERSE OPERATIONS?

Let’s take a look at a simple equation

Step 1:+ 5

Answer:

125 y+ 5

17y


1212

125 y

12517

HOW DO WE SOLVE EQUATIONS WITH INVERSE OPERATIONS?

Let’s take a look at a simple equation

Step 1:

Step 2:

25

Answer:

7525 W25

25

75W

3W


7525 W

75)3(25

7575

How do we solve equations with inverse operations?

• Let’s take a look at a simple equation

Step 1:

Step 2:

(16)

Answer:

416

A

(16)

)16(4A

64A


44

416

A

416

64

1 Step Equation

X + 11 = 9 X - 37 = 52 3X = 72-11 -

11X = -2

3 3

X = 24

1

1

20 + h = 41 17 - s = 27

1 Step Equations Continued…X / 5 = 10X / 7 = 46X = 42

25

P = 34

3 / s = 21

Multi Step Equations

Solve:

8m – 10 = 36

423

31176w

8m – 10 = 36

8m = 468 8

m =

+ 10 + 10

Multi Step Equations

5x 2 = x + 4 Solve:

5x 2 = x + 4

Notice that there are variables on both sides

5x = x + 6

Get rid of the -2 on the left side

Simplify

5x = x + 6Get rid of the x on the right side4x = 6Get rid of the coefficient of x

4 4

23x = Simplify

Simplify

+ 2 + 2

– x– x

Solving a Proportion

• Solve the proportion below

60

126

C)12()60(6 C

C12360 12 12

C30

Solving a Proportion

• Solve the proportion below

852

13 a )(52)8(13 a

a52104 52 52

a2

Checking the Solution to a Proportion

• Let’s check the solution to the proportion we solved on the last slide

852

13 a

852

132

4

1

4

1

Using Proportions to Solve Problems

• You get 46 miles to a gallon of gas. How far can you go on 16 gallons of gas?

m

16

46

1 )16(461 m

736m

APPLICATION OF LINEAR EQUATION IN DAILY LIFE

the following are several terms commonly used in narrative problem and how to write them.

NO Terms How to Write

1 The sum of m and n m + n

2 The difference between m and n m – n

3 Product of m and n m x n

4 Quotient of m and n m : n

5 The inverse of m

6 Inverse of the sum of m and n

7 Square of sum of m and n ( m + n )2

8 Sum of square of m and n m2 + n2

9 Square of difference m and n (m – n )2

10 Difference of square of m and n, m2 > n2 m2 – n2

11 Square of m m2

Equiations and inequalities

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