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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.

toggle answer

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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