Algebra Lesson - Transposition

In these lessons, we will learn one of the basic techniques of simplifying an algebraic equation so that we can eventually solve the equation.

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Related Pages
Basic Algebra
Combining Like Terms
Solving Equations
More Algebra Lessons

This may be your first algebra lesson. In case you are rather uncomfortable with algebra, you may want to first go through Basic Algebra - An Introduction, which would give you a good foundation before this lesson.

Algebra Lesson - Transposition: Some Examples

The following are some examples of Algebra Transposition. Scroll down the page for more examples and step by step solutions.

Algebra Transposition

This Algebra Lesson introduces a technique known as ‘transposition’. This is the most common way to solve algebra equations. A quick review here of the basic principles - all equations have two sides: a Left Side (LS) and a Right Side (RS). In the example below 3x + 4 is on the Left Side of the equation and 31 is on the Right Side of the equation:

3x + 4 = 31
LS      RS

The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity).

So, to solve this equation, first subtract 4 from both sides of the equation. This will get rid of number 4 from the LS

3x + 4 - 4 = 31 - 4

That will give us:

3x = 27

Now, looking at the LS we have 3x. So we need to divide it by 3 to isolate x, and we need to do the same to the RS.

\(\frac{{3x}}{3} = \frac{{27}}{3}\)

Now that gives us:

\(x = \frac{{27}}{3} = 9\)

Check Our Answer:
Now, we have x = 9. We can substitute this value in the original equation to check if our answer is correct:

3x + 4 = 31
3 × 9 + 4 = 31
27 + 4 = 31
31 = 31

So, our answer x = 9 is correct.

That’s the algebra lesson on transposition. Now, you are ready to review some examples to further develop your understanding of transposition.

Transposition (Rearranging Equations) - Introduction

What is transposition? What is it used for?

Transposition (Rearranging Equations) - 1

How to transpose (or rearrange) equations?
How to solve equations?

  1. Remove fractions
  2. Remove brackets
  3. Move added/subtracted terms
  4. Divide by the number next to the letter

Transposition (Rearranging Equations) - 2

Include added and subtracted terms

Transposition (Rearranging Equations) - 3

Add brackets to the set of equations that we’ve already learned how to transpose

Transposition (Rearranging Equations) - 4

Include all the steps

Algebra Lesson - Transposition: Practice Questions

Algebra Worksheets and Practice Questions

Having completed the practice questions, you are now ready for other algebra lessons, like Substitution.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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