Learning to Solve Algebraic Equations

There are various disciplines in the field of mathematics. It is a very interesting subject to learn and can be fun. To simplify algebraic equations, the concept of equations has to be clear. In equations there are both constants and variables present.

There is difference between both these. The value of constants almost remains same throughout but the value of variable changes. Equations can be solved with the help of various methods. The method of elimination can also be used.

It is very simple to use and can be easily learnt. One of the variables is eliminated to find the value of the other variables in this method. The equation algebra can be an interesting subject to learn if one has interest to solve equations. Sometimes equations in algebra can be very tricky to solve and one has to be careful while solving them.

The concept equations algebra is nothing but the equations that are present in this discipline of mathematics. There can be various methods to solve these equations. Many methods are available online to solve them. These methods can be easily learnt and applied while solving them. The algebra equations online will help in explaining the concept better.

Once the equations are solved, various values of the variables present in the equations are obtained. These values must satisfy the whole equation; otherwise they cannot be taken as the solution of the equation. These solutions must be feasible and must be acceptable.

An equation can have more than one solution. Once the solutions are obtained, it can be checked whether the solutions are right or not. Sometimes even complex numbers can be obtained as part of the solutions. In a complex number there is an imaginary part attached to it. There is also a real part also to the complex number. Both the real and imaginary part forms the complex number.

The art of solving equations can be very interesting. The equations can be of different types. There can be linear and quadratic equations. The difference between the two is only in their degree. The linear equation is very simple to solve compared to the quadratic equation.

The linear equation can be easily solved with the help of basic arithmetic operations and the principle of transposing. Once these concepts are known the linear equations can be easily solved. Once solved the solutions could be easily checked.

Boolean Algebra Tutorial

This Boolean Algebra Tutorial gives us a holistic view of what Boolean functions and calculations are and will surely aid in solving many mathematical problems related to Boolean algebra
Basic operations in Boolean algebra are as follows:
Conjunction: also denoted by an inverted V this operation basically is similar to the intersection operation. In this we have a specific formula. Actually this formula is derived by basic algebra intersection operation:
A intersection B = A + B – A V B - - - - - - -(1)
Here V is the union operation.
In Boolean Algebra we only deal with true or false here. So anything that is not true will be a false. We can also denote it by zero and one. Here one will denote a true and zero will denote a false.
Now let us state the complimentary operation. This is also called as the negation operation. It is a singular operand operation. That is in this we will need just one operand to calculate the result. Let us take an example. Say A = True. Now negation A will be false. This operation can be stated as :
Let A = True;
~ A
Output A. Now the value of A will be false.
Union operation has already been discussed. In Boolean we have certain Boolean Algebra Rules to be followed for the same. Let us take a quick look at them.
True union True = True
(True union False) or (false union true)= True
False union False = false

Similarly for intersection we have
True intersection true = true
True intersection false = false
False intersection false = false
As we can see both the operation are just opposite to each other. These are Boolean form of algebra rules. Let us state them in a more simplified way.
A + 1 = 1
A + 0 = A
A . 1 = A
A . 0 = 0
So it is all about the multiplication or the dot product and the addition with zeros and ones. A here can have any value that is one or zero. Boolean Algebra Examples can be:
Let a = 1
B = 0 so a . b = 1 . 0 = 0
Similarly let b = 0, ~ b = 1. This is an example of complimentary operation.
Other rules for the Boolean forms are:
~(~A ) = A
A + ~A = 1
A. ~A=0
~(A+B) = (~A) .(~B)
~(A.B) = (~A) + (~B)

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