Students have many difficulties in algebra and do not know how to solve algebraic equations. The equations are required to simplify to get the right answer. If you have any difficulty in the simplification of linear equations, you should know the simple process to simplify it. An easy process can bring a right solution of the problems on this topic quickly. To understand algebra, you should learn how to solve different types of algebraic equations. You should able to simplify algebraic equations and to find the value of a variable.
How to identify a linear equation?
Algebraic equations are used in many fields of mathematics. Linear equations are the algebraic equations which give a straight line on the graph. Basically, it has two variables, and if you plot a graph using the equation, you will obtain a straight line. There are so many different forms to write these algebraic equations. But most common form has variables like x or y and constants like 3 or 9 or c.
Case 1: some examples can help you to understand these equations as given below;
3y + 6 = 5x,
3( x + 1 ) = y – 2
x/2 = 3
5y – 6 = 0
Case 2: Normally, the variables do not have exponents or square and cube roots. Like x^2-2 = 0 and 4√y – x = 8
So, the equations listed in case 1 are the linear equations whereas in case 2 are not these equations. Now, you can easily find whether an algebraic equation is linear or not.
Here, a simple method to solve the problems of single variable linear equations is given. You can use this method for solving the equations that have a single variable.
The simple process to simplify the linear equation
· Use the least common denominator to eliminate any fraction, if the equation has a fraction. Multiply both sides by the LCD to simply the equation.
· Then, simplify the both sides of the linear equation. For the simplification, clear out the entire parenthesis and also combine the like terms.
· The next step is just to put all the variables on one side and all the constants on another side of the equation.
· The last step is to solve the both sides by addition or subtraction.
Here is an example following the above steps. You can see this example to get a good method for simplifying equations.
7(x – 2) + 21 = 6 x is the problem and solution is given below
7x- 14 + 21 = 6x
7x – 6x = 14 – 21
x= -7 is the right answer.
Many people do not verify the answer, but it is also important to verify the answer. This is very helpful you to identify that you have a right solution or not. It is useful to find your mistake. Put your answer in the original equation in the place of the variable (here, ‘x’) and then cross verify by solving it. There are so many other methods to simplify such equations. The substitution method is the method to solve the linear equations that have two variables.