Algebra with Subtraction
(KS3, Year 7)
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 Subtraction?

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

algebra subtract 1 In the equation above, the x represents a number. In words, the equation means "x minus 4 equals 4". To solve the equation, we have to find the number that, when you take 4 away from it, equals 4.

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 rearranging 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 subtract 2

2

Find the opposite thing to get x on its own. The opposite to subtraction is addition, 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 subtract 3
algebra subtract 4 This is the solution:

x equals 8

Lesson Slides

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

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

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

scales rebalanced subtract

Swap the Sides, Swap the Signs

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

algebra subtract 1 mini algebra subtract 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.

  • Each falling equation has a correct answer and a wrong one.
  • Click on the correct one to score points and to make the equation disappear.
  • If you click on the wrong one (or do not click), the equation will fall to the bottom.
  • The wrongly answered or unanswered equations will start to build up.
  • When the screen is full, you're toast.
  • Good luck!
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This page was written by Stephen Clarke.