Equation Solver – A Guide to Solve Equations One by One

Equations seem to be a tough mathematics concept for many students, but it is not. Once you understand the right and proper concept to solve the equation, it becomes an interesting topic for you. Today, we are going to see certain techniques via which one can easily solve a linear equation. So, let’s start it: 

Solving equations

Equations consist of variables and constant terms. We have to find the value of given variable for example x. Let’s understand it with an example: 3 + x = 7

 In the given equation, we need to solve for X.  To solving this simple equation, we need to arrange the “Like terms” on both the sides, i.e., L.H.S and R.H.S.  After the arrangement of like terms, we get 4 as an answer:

3 + x = 7

x = 7 – 3

x = 4

There is only one variable, i.e., X in the equation and we have got two numbers. So, we have to arrange the numbers on one side. While changing the sides of constants and variable terms, make sure to change their signs as well. In the above example, x remains on L.H.S. However, we have shifted 3 on the R.H.S. After coming on the R.H.S, its sign becomes negative to positive and same goes with the variables also.

1.  Solving equation (using subtraction & addition properties)

 We have equation 3x + 3 = x +15, let’s start solving it:

3x + 3 = x +15

3x - x = 15 - 3

(In this step, we have arranged “like terms,” and thus terms with variables shifted on L.H.S and constant terms on the R.H.S.)

2x = 12

(After solving them, we have got 2x and 12.)

x = 6

After further multiplications, we have got answer 6 which is the right value of X.  Is it simple right? So, no let’s move on to the multiplication method.

2. Solving equation (Using multiplication property)

We solve equation 

plus going to discuss some important point’s one need to consider while using multiplication property.

I am going to explain it in a very simple way. In this method, we use multiply both the sides by using a nonzero quantity to get the answer. Let’s see how to do it? 

(In this step, we have canceled 4 as the numerator gets canceled by the denominator because of being a multiple of 4.  However, on the R.H.S we need to multiply 4 from 3 which results in 12.  Yes, you can direct multiple 4 from 3 but do this only when you understand the concept properly.

x = 12

When we solve for x, we got to answer 12.  The method is very easy, however; make sure to practice it more often for perfection.

3. Solving equation (using division property)

Let’s take an example 4x = 12. Now, in this one, we are going to divide the terms by a nonzero quantity to get the answer.

(In the above step, we have divided both the sides by 4 and thus got 3 as the value of x. talking about the L.S.H then 4 in denominator and numerator got canceled. On R.H.S, number 12 is divided by 4, and we got to answer 3. 

The above three concepts are easy to practice, so go for the concepts and improve your linear equation solving skills.