An equation is a numerical statement that has an ‘=’ sign.
Example:
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One of the numbers has been written as a letter. We solve an equation when we calculate the value of the letter.
Since we know that 
we can say that 
. The number 
is the solution to the equation above.
Equations come in many forms.
Linear equations are equations that we solve by adding, subtracting, multiplying or dividing only.
Solve a ‘one step’ equation
A one-step equation can usually be solved by number recall/logical thinking. Multi-step need the ‘completing and balancing’ method. This applet illustrates the logical thinking and the completing and balancing methods.
Solve a ‘two step’ problem
An equation such as 
is often referred to as a two step problem. The value 
has been multiplied by 3, and then 5 has been added. Two operations. That requires two reverse operations to figure out . Here are three techniques for figuring out the value :
- Guess and check. This is a good approach if the unknown is a simple whole number.
- Work backwards. This is a good approach for two step equations, but not for more complicated equations.
- Completing and balancing. This is what algebra is named for. Its when we “do the same to both sides” to keep the balance. This method works for all kinds of complicated equations.
Video: Mathantics Scroll to ‘Algebra Basics Part 1’
Printable: corbettmaths equations
Online interactive: transum maths equations
Solve Equations with letters on both sides
It can be helpful to follow some predetermined steps to solve these.
- Expand any brackets, simplify each side if necessary;
- Add or subtract the term from one side so that there is an term on one side only;
- Continue as before for two step equations.
There could be a better approach than these three steps – it really depends on the equation you’re solving. Its neat to figure out your own way to solve things.
Printable Corbettmaths, letters both sides
Online interactive letters both sides Transum maths