Solving simple equations

In an equation, letters stand for a missing number. To solve an equation, find the values of missing numbers. A typical exam question is:

Solve the equation 2a + 3 = 7

This means we need to find the value of a. The answer is a = 2

There are two methods you can use when solving this type of problem:

• Trial and improvement
• Using inverses

Trial and improvement

This method involves trying different values until we find one that works.

Look at the equation 2x + 3 = 7

To solve it:

Write down the expression: 2x +3 = 7

Then choose a value for a that looks about right and work out the equation. Try 3.

a = 3, so 2 ×3 + 3 = 9

Using 3 to represent a makes the calculation more than 7, so choose a smaller number for a.

Try a = 2, then 2

2 × 2 + 3 = 7

Which gives the right answer. So a = 2

Be systematic in your approach:

1. choose a number
2. work it out
3. then move the number up or down

However, sometimes the answers are negatives or decimals, and the trial and improvement method will take a long time. Luckily, there is a better method.

Using inverses

The best way to solve an equation is by using 'inverses', or undoing what the equation is doing.

To use this method to solve equations remember that:

• Adding and subtracting are the inverse (or opposite) of each other.
• Multiplying and dividing are the inverse of each other.

This method is explained in the next pages. But here for now is how to solve the question in the above example using inverses:

• First write down the expression:
• 2a + 3 = 7
• Then undo the + 3 by subtracting 3. Remember, you need to do it to BOTH sides!
• 2a + 3 - 3 = 7 - 3
• so 2a = 4
• Undo the multiply by 2 by dividing by 2 - again on both sides:
• 2a ÷ 2 = 4 ÷ 2

The answer is: a = 2