Learn to Solve a Linear Equation Perfectly

Mathematics is known to be a subject with lots of interesting facts with it. There are many who love to understand the subject deeply and know some more excellent facts about it. Algebra is the most important part of mathematics with some of the most interesting methods and formula. To be perfect in the subject one needs to be perfect with algebra.

Equations constitute some of the basic components, there are many who search out some of the best ways to get perfect in solving equations. If you are able you solve the equations well, then you can handle algebra very easily. Therefore here we are going to deal with the simplest, linear equation and the best ways to solve it correctly.  By the time you will get to know some more interesting tricks while solving such problems.

Linear Equation
Linear Equation

Thorough Basics

Before we move further, everyone should remember the importance of basics. If you are clear with the basics then only you will be able to handle the complex problems perfectly. Therefore it is the best that before moving on to the complex problems learn the basic tricks and formulae well. You need to use the right formula at the right place. You will soon be able to interpret this when you practice the problems regularly. Therefore have a look at your lessons and practice daily. This way you will surely be able to deal with algebra perfectly.

Solving a linear equation

Isolating the variable is the major part in the process of solving the linear equations when you get answers in the form y = 6 or x = 7. Here, the variable is brought to itself or is separated from the rest of the equation. But the question is, How to do this? Well, this may depend on several different factors. We will have to perform exactly the opposite of the operations that are done in the equation. This way you will be able to get the initial equation. Like if something is added we will subtract the same, or if something is multiplied, we will divide the same. All this has to be done considering the LHS and RHS rules. Here is the example of a one-step equation:

Suppose, 4x=8 ; Now to isolate the variable x, we will have to bring it to the other side which will result in the change of operation. Further, it will be:

x=8÷4 ; Therefore, x=2 . Thus isolating the variable will make it easy for you to get the answer.

A two-step equation

Now let’s see a two-step equation say, Solve 2y−7=13. The noticeable fact here is that the variable y is first multiplied by 2 and then 7 is subtracted from it. Therefore to cancel these effects, the solution will move like:

2y-7+7 = 13+7 (Add 7 to both sides as per the LHS and RHS rule) Now,

2y = 20 ; Now solving the equation further,

2y⁄2 = 20⁄2 (Divide 2 on the two sides of the equation) Thus,

y = 10

This way you can easily solve and get perfect with any kind of linear equation.

Subtracting Fractions

The procedure of fraction addition is more or less the same as that used in the subtraction of fractions. This implies that if you have the know-how of adding fractions, you will have an easier time subtracting them. Subtraction of fractions is also one of the most common operations that we are likely to come across in many mathematical computations. All the same, if you have a problem subtracting fractions, there is absolutely no need to worry because what you need is only a few steps and procedure away.

To begin with, it is important to understand the structure of the fraction. A fraction can either be proper improper or mixed. In cases where you are required to perform subtraction of improper fractions, the first step should be to change it into an improper fraction first. A fraction has basically two numbers. One on top and the other at the bottom. The one on top is called the numerator, and the one at the bottom is the denominator. For example:

Given a/b, a is the numerator and b are the denominators.

Having understood the structure of a basic fraction, we shall consider two methods that can be used to subtract fractions basing on the number of fractions being subtracted. These methods require the understanding of the structure of a fraction.

Method of Common Denominator

Method of Least Common Denominator

  1. Method of Common Denominator

This method is well applicable when you are subtracting one fraction from another, meaning, you are dealing with two fractions only. Since by now we know the meaning of a denominator, it will also be-be helpful to understand the meaning of “Common Denominator.” What is a Common Denominator? When the denominators of the two fractions in question are the same or identical, we say that there exists a common denominator.

Therefore, the main aim of this method is to ensure that the denominators of the fractions are the same before performing the subtraction. When the denominators are not the same, subtraction cannot be done. How do we then ensure that the fractions have the same denominators? Multiply each fraction – the numerator and the denominator – by the denominator of the other fraction.

For illustration consider;

a/b – c/d = (a*d)/(b*d) – (c*b)/(d*b)

Once the denominators of the two fractions is now common, (b*d), the ‘new’ numerator are simply added.

Example; 1/2 – 1/3

(1*3)/(2*3) – (1*2)/(3*2) = 3/6 – 2/6 = 5/6

 

  1. Method of Least Common Denominator

This method is used when subtracting two or more fractions. The knowledge of the Least Common Multiple (LCM) is needed in this method. The LCM of the denominators is determined and used in the calculations. To find the LCM of the denominators, follow the steps below;

List the multiples of each denominator

Select the multiples that are common – appearing for all the denominators

Choose the smallest among the common list of the multiples. This is the LCM

After getting the LCM, divide the LCM by each denominator and multiply the result by the numerator of each fraction separately before you proceed to simply subtract the ‘new’ numerators and using the LCM as the denominator. Simplify the resultant fraction.

To clearly illustrate the long theory, we will need an example;

Question; 1/2 – 1/4 – 1/5

List the multiples of each denominator

2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22…

4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40…

5 = 5, 10, 15, 20, 25, 30, 35, 40…

Select the common multiples

20…

Choose the smallest = 20. This is the LCM.

[(1*10) – (1*5) – (1*4)]/20 = 9/20.

Want to know how Factor Calculator Works?

Factor calculator tries to simplify the any given quadratic equation. The equation is normally in the form of . The calculator then walks it way down until it gets an answer. The values of a, b and c are always known while that of x has to be solved. In this scenario, x is the variable, while a, b and c are the numerical coefficients of the given quadratic equation. One more thing, “a” should never be equal to zero otherwise the equations ceases to be a quadratic equation but instead becomes a linear equation.

So, for factor calculator to work effectively using the factoring method, the equation should be factor able otherwise another method will have to be deployed in order for you to get an answer of the value of variable x. when I say factor able, I mean that there have to be two numbers that have to multiply to the equal constant value of “c” and at the same time these two numbers need, to sum up to the numerical coefficient value of “b” the numbers are called the factors of “c”.

Illustration by example

People always tend to remember how something works when they have been shown an example and have also tried another example by their selves. So for you not to forget, I will show you two examples but make sure you go and look for other examples on your own.

Example 1

You have been told to factor 

Which two numbers can I multiply them together and get -4 and at the same time sum them up to get 3? They should definitely be 4 and -1.

Therefore, when substituted, they should be

The answer is (x -1) (x + 4). You can double check the answer by expanding what you got. Always, it should lead you back to the initial quadratic equation.

Example 2

Try and factor 

a*c = 6*-6 = 36 and b = 5.

The positive factors of -36 are; 1, 2, 3, 4,6,9,12,18 and 36

But the product of the two numbers is -36 and the sum is 5. It, therefore, one of the numbers has to be negative in order to satisfy this equation.  The best combination to satisfy this will thus has to be

-4 and 9, such that -4 * 9 = -36 and -4 + 9 = 5

Substituting 5x will result in an equation like this

From there, we can then factor the first two and then the rest.

This is what you should get if you are doing it on your book,

2x (3x-2) +3(3x-2). Our common factor here is (3x-2), and thus the final result should be

(2x+3) (3x-2).

You can try to expand it on your own. The answer should be equal to our first or original equation. If not, then you may have missed something along the way. I urge you to go retrace your steps and find out where you went wrong.

You can always go online and look for tutoring sites. The best that most people visit is quickmath.com. It is really cool.

How to use a Factoring Calculator

What is a factoring method in mathematical aspects?

First, it is important for us to understand what a “factoring” means in mathematical point of view. It means that two numbers have to multiply to equal constant term “c” and yet again sum up to “b” the coefficient on the x term. This method is used to solve quadratic equations that are factor able. So, the factoring calculator tries to solve the equation of it as long as the right values of the coefficients have been fed to that calculator.

Normally, the quadratic equation takes the form of  whereby the values of a, b and c are known while that of x has to be solved or obtained from the equation after it has been solved. In other words, it is safe to say that a, b and c are the numerical coefficients of the given quadratic equations.

To understand the factoring formula better, it is best to illustrate it using an example.

Solving quadratic equations using factoring method

We can take an equation like  and have been told to factor it.

First, we have to find the factors of 6 that add up to 5. But because we can write 6 as the product of 2 and 3, and the two also add up to 5, i.e. 2+3=5. Then, I will have to use 2 and 3 instead of the initial 6.

The above polynomial can be simplified further into the form of (x + m) and (x + n)

Therefore, it is all right to rewrite is this way (x + 2) (x +3).

= (x + 2) (x +3). You can leave it there or continue to get the values of x, which will be

X = – 2 and x =-3 However, this really won’t change anything. So you can leave it at the (x + 2) (x +3) point.

We can take a look at one more example for you to understand it clearly.

Factor,

The best way to approach such the problem is to apply the differences of squares rule which is

=(x + y) (x – y)

Therefore, = ((x – 2)-3) ((x – 2) +3). Simplifying it further will land us on these solutions:

(x – 5)(x + 1)

These two examples have been clearly explained. You can look for many other examples online or on books. There is this website that will save you a lot of time since it has many examples that have been explained step wise. The site is www.quickmath.com. You can visit the page and look for the factoring page within the home page. When you click on us, you will be redirected to a web page that contains the information I am talking about.  You can also raise the alarm if you think the answer they gave is not correct. You will have to send them an email and clearly, tell them what you think is the right answer, and I am sure they will update it immediately.

Add Improper and Mixed Fractions in Seconds

Adding the fraction is easy and simple. But it becomes hard when you have to solve tough and complicated fractions. Most of students do it in simple way and some are using traditional tricks and methods to solve. This will take more and more time to add the large and complicated fractions. Do you want to get efficient way to add fractions? You can get best one for accomplishing your needs. There are various tools and option of software available for you to use it for your reasons. You can choose the best and unique features in software for adding fractions. The online application you solve your issues is best and convenient way. There is compatible software for your devices you can hire to reduce study time.

Adding Fractions
Adding Fractions

To solve the large fractions take long time and after that you find that the answer is not correct then you realize you wasted your time. You have to start the same question at starting points. Get rid of these problems and hire best study software for mathematical problems. You can maintain your needs in better manner. If you are facing any kind of issues related to adding fractions and for more like using formulate then you can get best solution in just few clicks.

  • Add proper fractions: there are different types of fractions. If you are working your homework and facing problems to add fractions again and again then you can choose the features online tools. The fraction with smaller numerator and larger denominator is called as proper fraction. It is very easy to solve with the help of featured software. You can get easy access for doing all functions for add the different numbers.
  • Calculate mixed numbers: while solving large and complicated equation many a time there are more functions requires for adding the mixed numbers. The number with whole number and fraction is called the mixed numbers. It is quite easy to get results for mixed number in couple of seconds. You can sort and do expression of adding fractions to get rid of and sort issues for taking long time.

Fast process and easy procedure to get results

When you are using the software for assist your issues to solve complicated questions and adding fraction for large equations then you need to save your time for further pending work. You have now options to get for your needs. There are several categories and tools available in software to resist the problems coming in between you and study. Reduce study time by using latest and advanced techniques along with your study. You can access fast while you are processing for your function at software. You have to submit your equation or adding fractions and there are separate to available and you just click on that tab after few seconds the results is on screen.

You can compare and crate graph for results at featured software. The software allows you to do various function for your wellness and to know the basic and aspects to gather general information. You can use the software for better preparation for future and increasing skills.

Math VS Magic

Does anybody here love math? I love math except when problems are given, and I am to solve it. Most of the time I keep on wondering, why do I need to keep on solving for x or  y or whatever letters my instructor chooses to. Then after submitting the assignment where I spent sleepless night figuring out the solution, the instructor would show the answer. Just like that, is it magic? How come I came up with a different answer? Maybe a lot of you our like me, doing everything I can to solve the problem but ends up doing it the wrong way.

Math is an exciting subject, especially when computing for money, right? But it could also become so complicated that it feels to be a burden. Well, the teacher says you are allowed to use your calculators for your home works, great isn’t it? Yes, if you understood how to do it step by step. But what if mathematical equations look like magic to you? A magician’s hat is presented empty (that’s the math equation), then the magician says abracadabra and viola you now have a rabbit in it (the instructor writes the series of letters and numbers then viola you get the value of x.) Math is similar to magic right?

Math
Math

There may be a lot of factors why I didn’t understand how to solve the problem, maybe I got confused with the whole process, or the instructor did not bother to explain how it happened, just like how magicians keep their magic a mystery, it just did.

Before I become carried away with magic, let’s go back to the home work that would allow you to use a calculator. So the challenge is even if you have this magic wand in the form of a calculator, you can’t still perform the trick because you don’t know how right? Here’s a secret that I would share, in order for you to pull off the magic successfully or in our case solve the math problem successfully, you will need two things, the magic wand (aka calculator) and the pixie dust. Now, maybe you’re wondering, pixie dust? Yes, and in our math case, our pixie dust is the websites like www.quickmath.com and others. This is the real secret to pulling off the trick.

In this site, you’ll have access to algebra calculator, fractional calculator, polynomial calculator, etc. a real math solver site where you can input the whole mathematical equation, and it calculates the answer. It also provides the step by step solution on how it derived the answer.

Solving math equations and formulas are now easy. Doing home works would be a breeze. But make sure to take time studying the process, you might get a perfect score with your assignment but get into trouble during exams, seat works and recitations. This is simply, a tool to assist you in understanding and solving math problems.

The more complicated the equation, the more amazing it gets. Go on, check out the site and be amazed on how it works like magic.

Functions that can be used in Online Calculators

When you are using an online exponent calculator, you will have all the functions that has to go into the problem, so all that you have to do is type in the numbers. You will be able to find the exponents for many numbers in this way. But if the exponent calculator does not display that key symbols, then you will be able to type it into the space provided. The number of which the exponent should be found should be entered first, and that will make it the base number. After that, the caret symbol should be entered after which the exponent value is typed. The exponent value in the exponent calculator will represent the number of time the base value should be multiplied by itself so that you can get the answer. You will be able to follow the same process for solving problems like GCF, LCM, expanding an equation and factorizing an equation. For all these problems the base value is written, and the exponent should be entered after the caret symbol. Once the problem is entered, you will be able to find the answer by clicking solve.

Exponent Calculator
Exponent Calculator

Some online calculators will have a function in which the problem can be entered, and if it is complex, then you will be able to get the help of a tutor or an online community for solving it. This is very useful for solving problems like integration, differentiation, matrices and much more which could involve a lot of steps and calculations. When you are entering the matrix, you can separate each value in the row by using a comma, and you will have to enter an underscore to separate the rows. All the values will be entered within a set of parenthesis.
If you have to use subscripts for problems in logarithms, then you can enter the variable that is the base outside the parenthesis and the subscript will be entered within. This type is used to specify the variable that you are using currently. Entering square roots will also involve a similar process in which you will type the number for which you should find the square root or the radicand inside the square root symbol that will be displayed on the screen. If you have to find the roots for other bases like cube root or root to the fourth power, then you should enter the radicand within the root symbol and the index value such as 3 or 4 should be specified outside the sign within brackets.
Coordinates will represent the points that you have to plot, and this will be very useful when you have to plot a graph. You will be able to type in coordinates by entering the values within brackets and then you can separate it with a comma so that the x and y-coordinate will be differentiating. Functional notation like f(x) will be entered the same way as coordinates, and it can be used for replacing the y variable. Many such functions can be used for solving all the equations.