Linear equation: Basic guide to solving each equation

This chapter is most important part of mathematics where you get to solve numbers of equations. Maybe you are the one who is afraid of this subject, but once you get the basic, you will find it amazing than any other chapters. Through this article, you can solve any Linear equation. You will get certain techniques which will improve you in solving multiple problems. These techniques involve rewriting of problems mainly in the form of symbols and simple terms. For example:

“Find that number which can give you 11 when added with 7.”

It may be written in several ways, for example, 7+? = 11, or maybe 7+n = 11, or 7+x = 11

And so on, you can take any term based on your choice and selection, but if you are solving equations through your book, then you will find more accurately x in place of any symbols like “?” or any other symbol. The above example, i.e., 7+x = 11 is called to be the first-degree problem. You can recognize first-degree problems when equation which contains variable with a maximum exponent of 1. The term placed at the left is to be maintained in such a way that equal sign can be placed on the right side. Thus, in the equation, you can see left contains “7+x”, while right contains “11”, where equality is created with the variable x.

Solving equations

When you solve any first degree problems, you get to know that equation may be false or true, and it only depends on what choice you are making for the variable x. Like the equation: 7+x = 11 will be false if any other number except four is substituted with this variable. For this equation, four is called the solution of the problem and the variable. You can get solution only if you are substituting the number from left to right in place of the variable.

Example: Determine if 0 is the solution of the equation

14x – 3 = 4x – 3

In this equation, you can substitute 0 with the x to check if the equation is correct or not.

Substituting it, you get 14(0) – 3 = 4(0) – 3 which is -3 = -3 or 3 = 3, so the equation is correct

Some other example: 2x – 3 = 8x + 6, check if equation is correct for -3

To check it, again substitute x with -3, then you will get: 2(-3) – 3 = 8(-3) + 6, which is -6 – 3 = -24 + 6, that is, -9 = -18, or 9 = 18 (here, you can see that left hand site does not equate with right hand side) hence, equation is not correct for -3.

Now, if you want to check what solution is correct for the variable to equate both sides of linear equation, then you can do some steps. Firstly, you should be sure to transfer variables and numbers on the other sides, like 2x – 3 = 8x + 6, to 2x – 8x = 6+3, that is, -6x = 9, where you get x = -9/3 as the solution. (You see through this example that when numbers and variables get transferred, change their symbols).

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Solve for X – Easy Methods to get the Value of X

If you are looking for different ways via which you could solve for x, then you are welcome here. The content is meant for those students who face problems while solving radicals and exponents in algebra. After reading this content, you will get the right method to solve it. So, let’s start this learning session.

Basic linear equation

We are going to solve simple linear equation 5x – 8 = x + 4 and find out the value of X.

Step 1: At first, we will arrange 5x and x on the left-hand side and 4 and on the right-hand side.

5x – 8 = x + 4

Step 2: After that, we will solve the arrange number and here is the further procedure:

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Important note: Before solving any equation, students should solve exponents if there is any to make the equation easy.

Solve it by isolating the terms (in case of exponents)

If you didn’t get it as what I meant by the word “isolating” then here is an explanation for you. It means that you should make one term disappear to get the value of X. The trick is quite popular plus makes the procedure easy. So, how to solve for x by this method?

Example: 2x² + 14 = 46

Step 1: In the above example, we are going to isolate term 14 and thus we ill subtract both the sides by 14.  Keep in mind that you should choose an opposite side for isolating a term, i.e., here 14 is positive and thus we have chosen (-14) in it.

2x² + 14 – 14 = 46 – 14

2x² = 32

Step 2: Now you see that number 14 has gone and now we can find the value of x easily. Here are its further steps:

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Now, we know that 16 is the square of 4 and thus we will square root both the sides and get:

x = 4

Solving fractions by cross multiplication method 

Fractions are easy to solve, by using multiplication methods we can get the value of X. So, here is the example:

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Step 1:  We will solve this by cross multiplication method where we will multiply 4) by 4 and 3 by 4.

(x – 4) (4) = (2) (4)

4x – 16 = 8

Step 2: Now we will combine the like terms like this:

4x = 8 + 16

4x = 24

X = 24 ⁄ 4

And finally, we get x = 6. The cross multiplication method is very easy but does not forget to reduce the problem into simplest form.

Solve for x using radical signs

For this one, you need to learn some basic concepts of radical sign or square roots. Now, let’s solve example

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Step 1: In the first step, we will isolate the number 5 by adding 5 on both the sides like this:

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Step 2: Now we are going to square both the sides:

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Step 3: Again, we will subtract both the sides by 7 so that 2x remain on the LHS:

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So, we have got the answer 9, and you can verify this answer by putting the value of x in the problem.

Hope so all the methods explained above let you solve for x easily and make your mathematics stronger.

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.