Learn the ways to solve linear equations

What is a linear equation? How to solve it? Here, in this article students will learn about linear equations and ways to solve it. The linear equation is a simple plain equation that contains simple variables with no square roots or fraction. It contains variables like x rather than complicated variables like x² solving them is simple and you can solve it in the same way you would solve the simple addition and subtraction.  In these equations instead of direct value, a variable is given. You have to find its value and then you will get the result.

However, a linear equation can vary from simple to more complicated expressions that take time to solve. More advanced methods are thus used for solving equations. To solve more complicated problems, students can use equation solver as well. Learn how to solve the simpler problems before we begin solving more complex problems.

Let’s learn through examples:

Example 1- solve equation x-9=3

Solution:

Here, the variable is x whose value we have to find. To solve for x, we need to eliminate 9 from x to find its value. To undo it, let’s add 9 to one side. Since the equation should be balanced on both sides, so add 9 to another side as well to make the balance. The equation will look something like this:

(X-9)+9=3+9

X-9+9= 12

Plus 9 and minus 9 will cancel each other, and thus we will get the value of x. So, x=12. This is called as addition-subtraction property.

Note- always remember that whatever we add or subtract at one side the same goes on another side to balance the linear equations. If you don’t add/subtract the same number to both the sides, then you will not get an answer.

You can also check whether the answer is correct or not. To check put the value of x in the equation.

X=12, on putting the value the equation will become

L.H.S:  12-9=3, R.H.S: 3, thus L.H.S=R.H.S

Value at both the sides is same; it means the answer is correct. If you get different values that means your answer is incorrect.

Some linear equations contain variables on both the sides. Let us learn how to solve such equations by taking next examples.

Example 2- 2x-4=x-6

Solution:

There are two ways to solve the above equation.

The first method - First, keep the numbers with x on one side and numbers without variable on another side by changing their signs. The equation will look like this:

                                                                                  2x-x=-6+4

Solving it will give this answer X=-2. To check it put the value of x in the original equation.

2(-2)-4= (-2)-6

-8=-8

Thus, a value on L.H.S and R.H.S are same. Hence the solution is correct.

The second method- you can solve the above problem using another method as well. Add 4 to both the sides to make the equation balance.

2x-4+4=x-6+4

2x=x-2

2x-x=-2

x=-2

The value of x is same as that we got from the first method. You can use the substitution method to check the correctness of the solution.

To solve more complex problems, you can take help of the equation solver as well.