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Maths

Solving equations

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In an equation, each letter stands for a missing number. To solve an equation, find the values of the missing numbers.

# 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.

Solve the equation: x - 6 = 9

To get x 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.

• x - 6 + 6 = 9 + 6
• x = 15
Question

Solve the equation 2y = 6 to find the value of y.

Answer

To get y on its own, we need to divide it by 2. As you already know, you must always perform the same operation on both sides of the equation.

• 2y ÷ 2 = 6 ÷ 2
• y = 3

The following is an example of a typical exam question:

Solve the equation: 2a + 3 = 7

Sometimes you need to use the inverses method more than once to solve an equation.

Here is how to solve 2a + 3 = 7 using inverses.

• 2a + 3 = 7
• Undo the + 3 by subtracting 3
• 2a + 3 - 3 = 7 - 3
• 2a = 4
• Then undo the multiply by 2 by dividing by 2 - again on both sides
• 2a ÷ 2 = 4 ÷ 2

The answer is: a = 2

Now try this question.

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