Transposition is a method to isolate the variable to one side of the
equation and everything else to the other side so that you can solve the equation.

Method 2: a shortcut trick that allows you to work faster

### Method 1

**Check the Answer**

Algebra - Solving Equations - Isolating the Variable

An equation is a symbolic statement that two algebraic expressions are equal.

To solve an equation means to find the variable or unknown.

The rule is that the same operation must be done on both sides of the equation to preserve equality.
Have a look at this video that clearly explains the steps to isolate a variable and solve linear equations (variables on both sides of the equation).

### Method 2

Shortcut Trick to help you solve equations (Variable on one side)
Shortcut Trick to help you solve equations (Variables on both sides)

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Two methods are covered here:

Method 1: as usually taught in schoolsMethod 2: a shortcut trick that allows you to work faster

A quick review of the basic principles - all equations have two sides: a Left Side (LS) and a Right Side (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 isolate the variable (or the unknown quantity).

For example:

5

x+ 8 = 3x– 6

We want to get rid of the number 8 from the left side.

So we subtract 8 from both sides of the equation.

5x + 8 |
= | 3x – 6 |
original equation |

– 8 | = | – 8 | subtract 8 from both sides |

5x |
= | 3x – 14 |
resulting equation |

Next, we want to get rid of 3*x* from the right side.

So, we subtract 3*x* from both sides of the equation.

5x |
= | 3x – 14 |
result from above |

– 3x |
= | – 3x |
subtract 3x from both sides |

2x |
= | – 14 | resulting equation |

Now, we want to get rid of the coefficient 2.

So, we divide 2 from both sides of the equation.

2x |
= | – 14 | result from above |

÷2 | = | ÷2 | divide both sides by 2 |

x |
= | – 7 | resulting solution |

Now check your answer *x* = –7 by plugging it back into the original equation.

5

x+ 8 = 3x– 6LS: 5

×(– 7) + 8 = – 35 + 8 = – 27

RS: 3×(– 7) – 6 = – 21 – 6 = – 27

LS = RS, answer is correct.

An equation is a symbolic statement that two algebraic expressions are equal.

To solve an equation means to find the variable or unknown.

The rule is that the same operation must be done on both sides of the equation to preserve equality.

In this method we isolate the variable by moving like terms to one side of the equation. To maintain the equality of the equation, when removing a term from one side of the equation we perform the opposite operation to the other side.

For example:

5

x+ 8 = 3x– 6

To remove + 8 from the LS, we subtract 8 from the RS

To remove + 3*x* from the RS, we subtract 3x from the LS

To remove the coefficient 2, we divide 2 on the RS

When you have grasped Method 2, it is faster because it allows you to perform several steps at the same time to isolate the variable.

For example:

5

x+ 8 = 3x– 6

Shortcut Trick to help you solve equations (Variable on one side)

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.