Easy Math of Linear (Equations and Inequalities) One Variable

Math of Linear (Equations and Inequalities) One Variable
Completion of the set of graphs of linear equations of the variables shown in a number line, in the form of dot (point).
example
Determine the completion of the set of equations
4 (2x + 3) = 10x + 8, if x
variables on the set of integers. Then, draw the number line
completion:
4 (2x + 3) = 10x + 8
8x + 12 = 10x + 8
8x + 12 - 12 = 10x + 8-12 (both sides minus 12)
8x = 10x - 4
8x - 10x = 10x - 4 - 10x (10x minus both sides)
-2x = -4
-2x: (-2) = -4 (-2) (both sides are divided by -2)
 x = 2
Thus, the solution set is {2}.

Easy Math of Linear Inequalities One Variable
In everyday life, surely you've come across or find sentences like the following.
a. Rebbecca weigh more than 52 kg.
b. Josh height 7 cm less than my height.
c. One of the requirements to be members of the Army is his height not less than 165 cm.
d. A bus can carry no more than 55 people.
How sentences are expressed in the form of mathematical sentence? To be able to learn to answer the following description.

1. understanding inequality
In order for you to understand the sense of inequality, try to remember back in elementary school about the matter in writing notation <,>,<,> , and not same.
a. 3 less than 5 written 3 <5.
b. 8 more than 4 written 8> 4.
c. x no more than 9 written x < 9.
d. Two times y is not less than 16 written 2y > 16.
Sentences 3 <5, 8> 4, x < 9, and  are called the inequality 2y >16 .
In general it can be written as follows.
An inequality is always marked by one of the following hyphen.
"<" For less than stated.
">" To declare over.
"<" to represent no more than or less than or equal to.
">" to represent not less than or more than or equal to.

2. Linear Inequalities One Variable
On the front you have learned that an equation is always marked with a hyphen "=". In this section you will learn the characteristics of an inequality.
example
Of the following forms, which specify a linear inequality with one variable.
a. x - 3 <5
b. A < 1 - 2b
c. x2 - 3x > 4
completion:
a. x - 3 <5
Inequality x - 3 <5 has one variable, namely x and rank 1, so x - 3 <5 is a variable linear inequality.
b. A < 1 - 2b
Inequality a < 1 - 2b has two variables, namely a and b, each of which rank 1.
Thus a < 1 - 2b is not a single variable linear inequalities.
c. x2 - 3x > 4
Due to the inequality x2 - 3x > 4 has variable x and x2, then x2 - 3x > 4 is not a single variable linear inequalities in Easy Math of Linear.

 

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Quick Math Methods ONE VARIABLE LINEAR EQUATION

Quick Math Methods ONE VARIABLE LINEAR EQUATION  

1. Understanding Similarities and Association of Settlement
Linear Equations in One Variable Note the open sentence x + 1 = 5.
Open sentence is linked by an equal sign (=). Next, open sentences connected by an equals sign (=) is called equality.
Equations with a single variable or a rank one linear equation of degree one is called a variable.
 

If the x in the equation x + 1 = 5 is replaced with x = 4 then the equation is true. As for if x is replaced numbers other than 4 then the equation x + 1 = 5 is false. In this case, the value of x = 4 is called the completion of the linear equation x + 1 = 5.
 

Furthermore, the completion of the set of the equation x + 1 = 5 is {4}.
Substitute the variable x resulting equation is true is called the completion of linear equations. Completion of the set of all sets of linear equations called linear equations settlement. Try to discuss with your friends instead of the settlement called linear equations.
One variable linear equation is an open sentence is linked by an equal sign (=) and only has one rank of one variable. General form of the equation variables linear one is ax + b = 0 with a X 0.

Quick Math Methods Example:
Of the following sentences, determine which is the linear equation of one variable.
a. 2x - 3 = 5
b. x ² - x = 2
c.1/3x = 5
d. 2x + 3y = 6
completion:
a. 2x - 3 = 5
Variables at 2x - 3 = 5 is x and rank 1, so the equation 2x - 3 = 5 is a linear equation of one variable.

b.x ² - x = 2
Variables in the equation x² - x = 2 is x rank 1 and 2. Since there are x rank 2 then the equation x ² - x = 2 is not a linear equation of one variable.

c. 1/3x = 5
Because the variables in the equation 1/3x = 5 is x and rank 1, then 1/3x = 5
a linear equation of one variable.

d. 2x + 3y = 6
Variables in the equation 2x + 3y = 6, there are two, namely x and y, so 2x + 3y = 6 is not a linear equation of one variable.

2. Association of Settlement One Variable Linear Equations by substitution
Completion of one variable linear equations can be obtained by substitution, is replacing variables with numbers corresponding to the equation into a sentence that is true.

Quick Math Methods example:
Determine the completion of the set of equations
x + 4 = 7, if x is a variable in the set of natural numbers.
If x is replaced natural numbers, is obtained
substitution x = 0, then 0 + 4 = 7 (one sentence)
substitution x = 1, then 1 + 4 = 7 (one sentence)
substitution x = 2, then 2 + 4 = 7 (one sentence)
substitution x = 3, then 3 + 4 = 7 (correct sentences)
substitution x = 4, then 4 + 4 = 8 (one sentence)
It turned out to x = 3, the equation x + 4 = 7 a correct sentence.
Thus, the set of the settlement equation x + 4 = 7 is {3}.

This series of Quick Math Methods ONE VARIABLE LINEAR EQUATION 

 

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Smart Math OPEN SENTENCE IN MATH Easy Methods

SMART MATH  >> Open Sentence in Math
1. Statement Smart Math
In everyday life we often see a variety of the following sentences.
a. Jakarta is the capital city of Indonesia.
b. Mount "Merapi" in Central Java.
c. 8> -5.
The third sentence above is a sentence that is true, because every person recognizes the truth of the sentence.
 

Then consider the following sentences. 

a. "Monas" is located in Jogjakarta.
b. 2 + 5 <-2
c. Sunset in the east.

The third sentence is a sentence that is false, because everyone does not agree with the sentence.
Sentences that can be determined truth value (true or false) statement is called.

Now consider the following sentences.
a. Apple fruit taste sweet.
b. Eat nutritious foods.
c. Learn diligently so you go up a class.
Can you determine the truth value of the sentence - the sentence above? Do you think the sentences are not statements? Why?

2. Open Sentences & Sentence Completion Association open Smart Math.

Can a sentence to answer the question "Indonesia is located on the continent of x". If x is replaced Asia then the sentence is true. As for if x is replaced Europe then the sentence is false. Sentences such as "Indonesia is located on the continent of x" is called open sentence.
a. 3 - x = 6, x member of the set of integers.
b. 12 - y = 7, y member of the set of natural numbers.
c. z * 5 = 15, z member of the set of natural numbers.

Sentence 3 - x = 6, x integer members would be true if x is replaced -3 and will be worth one if x is replaced numbers other than -3. Furthermore, x is called a variable, while the 3 and 6 are called constants.

Try to determine the variables and constants of sentence 12 - y = 7 and z * 5 = 15 in the above example.
Open sentence is a sentence that contains a variable and unknown truth value.

A variable is a symbol (symbol) on the open sentence that can be replaced by any member of the set that has been specified.
The constant is a fixed value (s) contained in an open sentence.
Now consider the sentence x2 = 9. If the variable x is replaced by -3 or 3 sentences then x2 = 9 will be true. In this case x = -3 or x = 3 is the completion of an open sentence x2 = 9. Thus, the completion of the sentence set x2 = 9 is {-3, 3}.
Completion of an open set is the set of all sentences replacement of variables in open sentences so that the sentence is true. That is SMART MATH Open Sentence in Math.

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Smart Math Quick Summary Algebra

Smart Math Quick Summary Algebra
 

1. Variables, constants, factors, as well as similar and not similar rates.
- A variable is a symbol that substitutes a number
its value is not known clearly.
- Constants are parts of an algebraic form
such as number and no load variable.
- The tribes are the kind that has a variable rate and
the rank of each variable are the same.
- Interest is not a type that has a variable rate and
the rank of each variable are not the same.
 

2. On the algebra, addition and subtraction operations
can only be done on similar tribes.
 

4. Multiplication between the two forms is expressed algebraically as follows.
(ax + b) (cx + d) = acx² + (ad + bc) x + bd
(ax + b) (cx² + dx + e) = acx³ + (ad + bc) x² + (ae + bd) x + be
(x + a) (x - a) = x² - a²

 

3. Multiplying a constant number k with the algebra
parts one and two tribes expressed as follows.
k (ax) = kax
k (ax + b) = kax + kb 

the two forms is expressed algebraically as follows.
(ax + b) (cx + d) = acx² + (ad + bc) x + bd
(ax + b) (cx² + dx + e) = acx³ + (ad + bc) x² + (ae + bd) x + be
(x + a) (x - a) = x² - a²
 

5. On the powers of the algebra of the two tribes, tribal tribes coefficient
determined by Pascal's triangle.
(a + b) ¹ = a + b
(a + b) ² = a² + 2ab + b²
(a + b) ³ = a³ + 3a²b + 3ab² + b³
and so on
 

6. Value of an algebraic form can be determined by
substituting any number on the variables
The algebraic form.
 

7. A fraction simplest form of algebraic say if
numerator and denominator have no factors fellowship
except 1 and the denominator is not equal to zero.
 

8. Results of operations of addition and subtraction on fractions
algebra obtained by equating the denominator,
then summing or subtracting the numerator.

 

That is there are 8 item Smart Math Quick Summary Algebra.

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Smart Math Methods "Algebra Arithmetic Operations" Easy way

Smart Math Methods algebra arithmetic operations 

1. Addition and reduction Algebra Shape On the algebra, addition and subtraction operations can only be performed on similar tribes. Totalizing or subtract the coefficients on similar tribes.Determine the sum and subtraction algebraic form following.a. -4ax + 7axb. (2x2 - 3x + 2) + (4x2 - 5x + 1)c. (3a2 + 5) - (4a2 - 3a + 2)Smart Math Solution:a. 7ax-4ax + = (-4 + 7) ax = 3ax 
b. (2x2 - 3x + 2) + (4x2 - 5x + 1) = 2x2 - 3x + 2 + 4x2 - 5x + 1= 2x2 + 4x2 - 3x - 5x + 2 + 1 = (2 + 4) x2 + (-3 - 5) x + (2 + 1)= 6x2 - 8x + 3c. (3A2 + 5) - (4A2 - 3a + 2) + 5 = 3A2 - 4A2 + 3a - 2= 3A2 - 4A2 + 3a + 5-2 = (3-4) a2 + 3a + (5-2) =-a2 + 3a + 32. 

Multiplication You need to recall that the integer multiplication effect / distributive properties of multiplication of the sum, ieax (b + c) = (axb) + (axc and distributive properties of multiplication the reduction, the ax (b - c) = (axb) - (axc),for any integers a, b, and c. This also applies to the nature of the algebra multiplication.a. Multiplying constants with the algebra of multiplication of a constant number k with the tribes and tribal algebraic form two stated as follows.k (ax) = kax k (ax + b) = kax + kb Hypotenuse angled triangle are (2x + 1) cm, while the length of the side of the elbow (3x - 2) cm and (4x - 5) cm. Find the area of ​​the triangle. Describe the following algebraic form, and then simplify it.a. 4 (p + q)b. 5 (ax + by)c. 3 (x - 2) + 6 (7x + 1)d. -8 (2x - y + 3z)

 Smart Math Solution:a. 4 (p + q) = 4p + 4Qb. 5 (ax + by) = 5ax + 5byc. 3 (x - 2) + 6 (7x + 1) = 3x - 42x + 6 + 6 = (3 + 42) x - 6 + 6 = 45xd. -8 (2x - y + 3z) =-16x + 8y - 24z

 b. Multiplication between two forms of algebraic as a constant multiplication by algebraic form, to determine the product of the two forms of algebra we can use the distributive properties of multiplication to addition and multiplication distributive nature of the reduction.Besides this way, to determine the product of the two forms of algebra, can use the following method.Note the multiplication of the algebra of two parts with the following two parts.(ax + b) (cx + d) = ax X cx + d + cx + b X b X d = acx2 + (ad + bc) x + bd

The above problem is to describe some of the workings of arithmetic operations in the form of algebraic subtraction, addition and multiplication, the ways solving already elaborated on smart math methods.

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