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.
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).