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# Solving equations

In equations a letter stands for an unknown number and you need find its value. You can solve equations with fractions. Trial and improvement involves substitution with different values.

# 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.
When you use this method you must perform the same action on both sides.

## Example

Solve the equation: To get on its own, we need to add 6. If you add 6 to one side of the equation, you need to add 6 to the other side of the equation:
• • QQuestion
Solve the equation to find the value of y.
This is an example of a typical question using inverses:
Solve the equation: Sometimes you need to use the inverses method more than once to solve an equation.
Here is how to solve using inverses.
• • Undo the + 3 by subtracting 3
• • • Then undo the multiply by 2 by dividing by 2 - again on both sides
• The answer is: Now look at this question.

Sometimes you will be required to solve an equation with unknowns on both sides of the equation.
Remember that whatever you do to one side you must also do to the other.
QQuestion
Solve the equation , and find the value of .
Look at another exercise below.

# Equations with brackets

If an equation has brackets in it, one method of solving it is to multiply out the brackets first, for example:
Solve the equation: • • Multiply out the brackets. Remember, everything inside the brackets gets multiplied by 3.
• • When you have multiplied out the brackets you get: • Next, undo the . In other words, do the inverse and subtract 6 from both sides.
• • So Therefore, to find out what b is you need to do the inverse of multiplying by 3 which is dividing by 3.
So .

# Fractions

How do we solve the equation ?
One way is to multiply everything by 2:   Or, alternatively, add and then multiply both sides by 2:   QQuestion
Solve the equation: .
QQuestion
A number is doubled and divided by 5. This has the same answer as 3 more than the number divided by eight. What is the number?
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