Learn Online Linear

A statement in which two quantities are equal is called an equation.

Introduction to learn online linear:

An equation of the form `ax+b=0, a!=0` is called a linear equation in the variable x.When the degree of the variable on both sides equal to one, then it is a linear equation. It has more than one variable.

Linear equation is the equation of the form y = mx + b. The above equation involves two variables namely  x and  y. Linear equation is a type of algebraic equation, which consists of all variables of degree one and constants. Examples of linear equations are

`5x = 10`  Linear equation of one variable

`4x+7y = 10` Linear equation of two variables

`3x +7y+9z = 11` Linear equation of three variables

Solution of linear equation: Any value ( or values) of the variable (or variables) which when substitued in an equation makes its both sides equal is called a solution (or root ) of the equation.


Types of linear equation:


Conditional Equation:
If the linear equation has the real roots, it is called conditional.

Ex:

2x + 5 = 7

7x + 3 = 10

Unconditional Equation:
If the roots are not real, it is called unconditional.

Ex:

5x + 8 > 1

4x + 4 < 1

Quadratic Equation:
Quadratic is  the second degree of the polynomial equation

Ex:

4x2 + 2x + 4 = 9

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Example problems on linear equations:


Ex 1: Solve the given equation 5x + 6 = 81

Sol:

Step 1:Given equation:   5x + 6 = 81

Step 2:Subtracting in both in 6:    5x + 6 - 6 = 81 - 6

Step 3:Simplification:      5x = 75

Ans:                   x  = 15

Ex 2 : Solve the given equation 8x + 5y = 90 and where is y = 2

Sol:

Step 1: Given equation:        8x + 5y = 90

Step 2:Substitute in y=2:   8x + 5(2) = 90

Step 3:Simplification:       8x + 10=90

8x = 90 -10

8x = 80

Ans:                x = 10

Ex 3 : Solve the given Equation: 9z + 25 = 4z + 65

Sol:

Step 1: Given equation:    9z + 25 = 4z + 65

Step 2:Subtracting both sides from 25:    9z + 25 - 25 = 4z + 65 - 25

Step 3:Simplification gives:        9z = 4z + 40

Step 4:Subtracting both sides 4z:  9z - 4z = 4z - 4z + 40

Step 5:Simplification gives:      5z = 40

Ans :    z = 8

Ex 4 :Solve 5x^2 + 2x - 3 = 0 for x.
Sol:

Step 1: Factor:   (5x - 3)(x + 1) = 0

Step 2:Simplification:   5x - 3 = 0, x + 1 = 0

Ans:  5x = 3,  x = -1

Ex 5: Solve: 4x + 9 > 97

Sol:

Step 1 Given equation:   4x + 9 > 97

Step 2  Simplification:     4x > 97 - 9,  then 4x > 88

Ans :   x > 22

Completing The Square Solve Online

Introduction:

Complete squaring is an application of algebra . this means the given equation is having solution, it means each equation is having one or more solutions. now a days technology is also uses in mathematics and the students is learning in online. the tutors would explain step by step for the students.

In this content we learned about the complete square problems. I like to share this Types of Triangle with you all through my article.


Complete Square Method Problems:


Example:

Solve the equation for x x^2 + 8x + 15 = 0
Solution:
There are three terms in this equation. One is constant (15) and the others contain variables (x^2 and 8x).

in this problem we do  factor the equation by determining what two numbers multiplied together gives a result of 15 when added give a sum of 8.

The factored equation looks like this:


(x + 3)(x + 5) = 0 (a)

the rule is First, Outside, Inside, Last (FOIL) method,

x^2 + 5x + 3x + 15 = 0 ----> x^2 + 8x + 15 = 0 (b)

We convert equation (a) into its terms and set each term equal to zero:

(x + 3) = 0 (c)
(x + 5) = 0 (d)

Now, solve each for x:

x + 3 = 0

subtract 3 from each side

x = -3

x + 5 = 0

subtract 5 from each side

x = -5

solutions are that x is equal to -3 or -5.

substitute x values in equation( 1 )

start with -3:

(-3)^2 + 8(-3) +15 = 0
(9) + (-24) + 15 = 0 This is a true statement so -3 is a solution.

Next,  -5:

(-5)^2 + 8(-5) + 15 = 0
(25) + (-40) + 15 =0 This is also a true statement so -5 is a solution.

So answer is x =  -3

and  x =   -5

Example2:Solve the equation for 2x^2 - 3x + 1 = 0

Solution:

2x^2 - 3x + 1 = 0

2x^2 - 3x = -1

x^2 - (3/2)x = -1/2

2a = 3/2

a = 3/4

a^2 = 9/16, so we add 9/16 to both sides:

x^2 - (3/2)x + 9/16 = -1/2 + 9/16 = 1/16

(x - 3/4)^2 = 1/16

x - 3/4 = +/- 1/4

x = 3/4 +/- 1/4

x = 1, 1/2

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Practice Problems:


Solve the equations for competing square
1)x^2 - x - 1 = 0
2)x^2-6x=16

Free Online Algebra Calculators

Introduction of free online algebra calculators:

Algebra is the part of mathematics which always deals with the study of operations such as addition, subtraction, multiplication and division. Algebra includes variables, constants, polynomials, exponents, terms and expressions. Basic operation of algebra is to balance the expression on both sides. This article free online algebra calculator briefly tells you the operations of algebra with various examples. I like to share this Polynomial and Rational Functions with you all through my article.


Examples of free online algebra calculators:


For free online algebra calculators consider the following examples.

Ex 1:   Simplify the expression:

10(a-5) + 7b-4(2a -3b+5) +15

Sol :        = (10a-15) + 7b-4(2a -3b+5) +15.

= 10a-15 + 7b -8a+12b-20+15.

= 10a-8a+7b+12b-15-20+15.

= 2a+19b-20.

Ex 2 :      Solve the equations:

x + 2y + 3z = 14, 3x + y + 2z = 11, 2x + 3y + z = 11

Sol :     Let the given equations be

x + 2y + 3z = 14  `|->` (1)

3x + y + 2z = 11  `|->` (2)

2x + 3y + z = 11  `|->` (3)

Consider the equations (1) and (3)

(1) `rArr` x + 2y + 3z = 14

(3) × 3 `rArr` 6x + 9y + 3z = 33

Subtract (1) –(3):

–5x – 7y = –19

5x + 7y = 19          `|->` (4)

Consider the equations (2) and (3)

(2) `rArr` 3x + y + 2z = 11

(3) × 2 `rArr` 4x + 6y + 2z = 22

Subtract (2) – (3):

–x – 5y = –11

x + 5y = 11              `|->` (5)

Consider the equations (4) and (5)

(4) `rArr` 5x + 7y = 19

(5) × 5 `rArr` 5x + 25y = 55

Subtract (4) – (5):

–18y = –36;                             i.e. y = 2

Substitute y = 2 in (5) we get

x + 5(2) = 11; x + 10 = 11;   i.e. x = 1

Substitute x = 1, y = 2 in (3) we get

2(1) + 3(2) + z = 11; 2 + 6 + z = 11 ; z = 3

The solution is x = 1, y = 2, z = 3.

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Practice problems for the free online algebra calculators:


Consider following problems for practice.

Pro 1 :  Solve the expression:  5(2a-3b+5c+7) + 21a – 3c + 34 + 12b.

Answer: 31a-3b+22c+69

Pro 2 :  Solve: 3x – 3y + 4z = 14; –9x – 6y + 2z = 1; 6x + 3y + z = 5

Answer: x = 1, y = –1, z = 2

These are the problems under the free online algebra calculators.

Algebra Calculator Online

Introduction to websites to learn algebra calculator online:-

In this article, we are going to learn

"what is the definition of algebra?"

"Where the algebra calculators are available online?"

"How to learn algebra from the calculators online?"


Definition of algebra:


Algebra is a  a branch of Mathematics in which the letters (generally alphabets) are used to represent members or numbers of a particular set. I like to share this learning pre algebra with you all through my article.


Websites which help us to learn algebra calculator online:


Here are a list of websites that help us to learn algebra online , the topics which can be covered using this calculator are also discussed here.

www.easycalculation.com:

This website will provide the calculator on Matrices (which is a concept of algebra). This will allow us to do the matrix addition, matrix subtraction, matrix multiplication, matrix inverse including determinant and ad joint of matrices.

www.algebrahelp.com:

This will provide us a calculator which can be used to solve equations.

www.myalgebra.com:

This is also one of the websites from which we can learn slgebra online. This website provides a calculator which allows us to enter the algebra problem and gives us the solutions.

www.quickmath.com:

This is an automated service which can be used to answer the common math problems online. This can be thought as an online calculator which can solve the equations and calculus problems automatically and instantly.

www.mathway.com:

This is an online Math problem solver which provides step by step solutions for the problems in  algebra concepts like basic maths and pre - algebra.

www.math.com:

This will provide us a basic calculator.

www.math-videos-online.com:

This is also one of the websites which provides online calculators and  helps us to learn algebra online.

This will provide graphic calculator, fraction calculator, compound interest calculator, factoring calculator, prime number calculator, greatest common factor calculator and least common multiple calculator.

www.calculatorsoup.com:

This will provide calculators to learn many algebra concepts online like cube roots, cubic polynomials, exponents, fifth roots, fourth roots, fractional exponents, radicals, radical exponents, square roots, quadratic equations etc.


Some other websites that help to learn algebra calculator online:


Other than the online calculators to learn algebra mentioned above, there are some other websites which are listed below.

www.univie.ac.at

www. solvemymath.com

www. myalgebra.com

www. sciencecentral. com

etc.

Factorization Solve Online

Introduction :

Factorization solve online guides you to understand the rules of factorization. To understand factorization, factorization solve online gives ample of time to grasp the concept. You can any time access online content and solve your doubts. Through factorization solve online you can 'by heart' the rules of factorization. Factorization solve online not only makes you clear all doubts regarding the subject, but also makes easy to remember it.

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What are the factors of 42? The answer is the factors of 42 are 6 and 7. Can 6 and 7 be factorized further? We will say yes because 6 = 2 x 3.. So now we can write 42 = 7 x 3 x 2. Here, 7, 6, 3 and 2 are called the factors of 42 because they can be multiplied by one another to get 42.

Similarly, to find the factors of an algebraic expression, we shall write it as a product of two or more algebraic expressions.

For example,

X(Y  +  Z) = X * (Y + Z)     -> Here the product of X and (Y + Z) is X(Y  +  Z). So X and (Y  +  Z) are called the factors of X(Y  +  Z). But if X(Y  +  Z) is written as XY  +  XZ, then XY and XZ are not the factors of X(Y  +  Z), because we do not get X(Y  +  Z) on multiplying XY and XZ.


An example of solve factorization online


What are the factors of 30?                                                                                                                                                                                       30 = 3 x 10 = 3 x 5 x 2

Similarly, factors of 2XY are:

2XY = 1 and 2XY

2XY = 2 and XY

2XY = 2X and Y

2XY = X and 2Y

2XY = 2, X and Y

Therefore the factors of 2XY are 2, X, Y, 2X, 2Y, 1 and 2XY itself. This is the example of factors of a monomial.

Factorization of binomials:

15x²y³ + 12x³y

Here for the constant numbers 12 and 15, the common factor is 3, so we write the binomial as

3(5x²y³ + 4x³y)

and the common variables are x and y. The exponents of x are 2 and 3out of which take x²(the least value of the exponent) out. So we will write                                                                                                                                                                                                                              3(5x²y³ + 4x³y) as                                                                                                                                                                                                                   3x²(5y³ + 4xy)

Similarly, the exponents of y are 3 and 1. Take the least exponent out. Thus, the expressions becomes

3x²y (5y² + 4x)


Another factorization example (solve online)


Let us look at another example:

20 a²b³ + 32 a³b²

The common factor of 20 and 32 is 4.

So 4(5 a²b³ + 8 a³b²)

Now looking at the variables, the common variable 'a' has exponents 2 and 3, and the common variable b has exponents 3 and 2. As we did in the previous sum, take out the variables carrying the least exponents, that is b² and a², to get

4a²b²(5b + 4a)

This is a completely factorized expression.

Online Algebra Terms

Introduction to algebra terms:

Online learning is a modern way of learning, which comprises of several advantages. The major advantage of online learning is that we can learn with comfort by staying in our home itself. Online learning will help us to improve our skills and knowledge level in a rapid manner. There are enormous amount of websites are available to learn in online. Online learning not only helps the students to improve their knowledge but also pay way for getting various information's related to a particular topic or subject. In math, various branches exist. Algebra is a main branch of mathematics. Algebra is a vast area in which various terms and definitions exists. Learning algebra terms finds it necessity in solving the problems. In this article, we are going to discuss few algebra terms, which are used in common.


Algebra terms:


Equation:

If the algebraic expressions contain equal sign, then it is referred as an equation.Let us consider 2x+y=6 as an equation since it has an algebraic expression with equal sign.

Degree of polynomial:

Degree of polynomial is the highest degree of any term present in the given polynomial.Let us consider x^2+2x+5 as a polynominal with the degree of 2

Direct variation:

Direct variation is the relationship between two given variables in which one of the variables will be a constant multiple of the other variable.

Domain:

Domain is the set of values of the independent variables for which a given function can be defined.

Factorial:

Factorial is the product of a given integer and all its smaller positive integers.

Focus:

Focus is a unique point, which is used to define and construct a conic section. I have recently faced lot of problem while learning Parallel and Perpendicular Planes, But thank to online resources of math which helped me to learn myself easily on net.


Additional algebra terms:


Function:

Function is a relation in which each and every element of the domain value  will have the corresponding range value.

Imaginary numbers:

If the complex numbers has no real parts, then it is referred as imaginary numbers.Here, `+-ib`

Leading coefficient:

The coefficient of the leading term in a given polynomial is referred as the leading coefficient.Let us consider 2a3 +6a here the leading coefficient is 2

Monomial:

A polynomial with a single term is referred as a monomial.Here 2x is a monmial since it has a single term.

Midpoint:

If the point lies halfway between the two given points, the point is known as midpoint.

Combinatorics:

The process of counting the number of elements in very large sets is known as combinatorics.

Common ratio:

In a geometric sequence, the common ratio is the ratio of a term to the previous term.

Teach Online and Get Paid

Teach online and get paid , teaching online has become so popular now a days and Tutorvista.com is the only company which gives proper training in all aspects of online teaching and certifies that,one is ready to tutor any student around the world ,they  have a highly qualified training team which is fully aware of the up to date technology changes. They do not ask for any registration charges it is absolutely free.There are so many dot com companies just by the name level and eye you just for the initial registration charges , once you register and pay online that is the end of it no more communication between you and that company BE AWARE. Tutorvista.com is the only online education company which offers tutoring for students from grade 1 to college level. I like to share this Area of Rectangular Prism with you all through my article.


What you need to teach online and get paid?


A post graduate degree in the preferred subject you like to teach , an under graduate degree also will do if you have experience in teaching , computer with basic easy to install software's and an Internet connection are the two basic things we need to get ready to teach online and get paid , of course you should posses the passion for teaching . Teach online and get paid according to the grade level you handle as the grade level increases pay also increases proportionaly . Understanding solving algebra 2 problems is always challenging for me but thanks to all math help websites to help me out.


Uses of teach online and get paid:

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