The Lesson

Algebra is using letters (or other symbols) to represent an unknown number. An equation that uses algebra is called an algebraic equation (note that algebraic is the adjective for algebra).

What Is an Algebraic Equation that Contains Addition?

An algebraic equation that contains addition is an equation with at least one letter being used to represent a number and with at least one addition.

algebra add 1 In the equation above, the x represents a number. In words, the equation means "x plus 4 equals 8". To solve the equation, we have to find the number that, when you add 4 to it, equals 8.

How to Solve This Equation

Question: What is the value of x in the equation below?

The key to solving an algebraic equation is to isolate the letter (or symbol) you are trying to find the value of. This is done by rearranging the equation so that you just have x on the left-hand side of the equals sign, and the answer on the right-hand side. In mathematics, you want to rearrange:

So you just have x on the left-hand side of the equals sign, and the answer on the right-hand side:

x equals The key to re-arranging an algebraic equation is:
Whatever you do to one side of an equation, you must do to the other side!

Step-by-Step Approach:

1

Look at what has been done to the x. algebra add 2

2

Find the opposite thing to get x on its own. The opposite to addition is subtraction, as shown in the table of opposites below:

algebra opposites The opposite of +4 is -4:

3

Do this to both sides of the equals sign.

algebra add 3
algebra add 4
This is the solution:

x equals 4

Lesson Slides

This slider gives another example of solving an algebraic equation that contains addition.

The Golden Rule of Algebra

The golden rule of algebra is: Whatever you do to one side of an equation, you must do to the other side! Think of a pair of scales. The equals signs means that both sides of the scales balance:

scales balance add If you do anything to just one side, the scales no longer balance and the equality no longer holds:

scales unbalanced add If you do the same thing to both sides, the scales return to balance, and the equality holds once again:

scales rebalanced add

Swap the Sides, Swap the Signs

Compare two of the steps in the step-by-step solution given on this page:

algebra add 1 mini algebra add 4 You can think of this of as 'switching sides, switching signs'. The 4 has moved from the left hand side to the right hand side of the equals sign; and has changed to having a + to a - in front of it. This can be done to any term that is an addition or a subtraction.

Equations ("Tetris" Game)

Here is an interactive game to help you learn about equations.

Tip: If the game is playing slowly, you can use the controls below to remove the background text and image to speed up the game.

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