How to Solve Linear Equations

Every algebra student needs to learn how to solve linear equations. It might take a little practice at first, but once you understand this crucial skill, you'll enjoy math class a lot more. Let GradeA help you:

What a Linear Equation Looks Like

The first step to learning to solve an equation is knowing exactly what one looks like. Here is a very common example:

3x + 2 = 5

So, a linear equation is made up of a couple numbers, a letter or letters, and an equal sign. It also has a plus sign in this case, but it could have a minus sign.

The goal is to find the value of the letter, or variable.


In other words, to solve an equation means to find the value of the variable so that the equation is true. In other words, we want to know what x stands for.

Make Solving Fun!

In some situations (word problems) the variable already stands for something - like someone's age, for example. However, in most cases you will be asked to solve an equation like the one above, where there is no real meaning behind the numbers. So, let's give them meaning!

I like football, so I am going to make my problem about football. I also like money, so we will use some of that too. Take a look at what happens. 3x + 2 = 5 becomes

Now our equation means "3 footballs plus 2 dollars equals 5 dollars."

Feel free to use other things besides football in your equation. What do you like? Is there a food that you really like? How about a favorite athlete or celebrity? A famous singer or rapper?

Use your imagination, have fun with it.  Learning how to solve linear equations will be a lot easier if you try to enjoy it a little bit.

Like everything, math is about having fun!


Think of an equation as a way of making a fair trade with a friend. You have the left side of the equal sign (3 footballs and 2 dollars) and your friend has the right side (5 dollars).


** Remember, we want to find the value of the variable - in this case a football. How much is ONE football worth?

How to find the value: Just do the opposite!

There are four major operations in mathematics: add, subtract, multiply and divide. They come in pairs:

  • add and subtract
  • multiply and divide

Understanding these operations are essential to learning how to solve linear equations.  Review our pre-algebra math problems if you need help.

How to Solve Linear Equations

Take your finger and cover up the part that has the variable. Just like it is shown in the picture below.


Notice how we took our finger and placed it on top of the 3 footballs.

Now, take a look at what you have remaining. We have...

+ $2 = $5

We need to identify what remains on the same side of the equal mark as the variable.

In this equation we have: + $2

Now, do the opposite! What is the opposite of + $2?

It is - $2. Make sure you do this to BOTH SIDES. For more information about performing operations on both sides, view our see-saw description of an equation.

Notice how we subtract $2 from each side of the equation. It is just like a simple subtraction problem that you have been doing for years.

Remove your finger to show what you are left with. We have ...



If 3 footballs are worth $3, how much is ONE football worth?

Each football is worth $1. and that is how we solve a linear equation

See? Learning how to solve linear equations isn't that hard. 

Learn other algebra topics or visit the GRADE-A hompepage.


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