How to solve simple algebraic equations

An equation is a mathematical expression that contains an equals symbol.
Equations often contain algebra. Algebra is used in Maths when we do not know the exact number in a calculation - this unknown value can be replaced with a letter.
We solve an equation by working out the value for one letter. To solve an equation we use the inverse operations to undo the equation.

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Find out how to solve simple algebraic equations with one unknown

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Click here to see a step by step slideshow.
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WHAT YOU NEED: A whiteboard, pens, a board rubber and a calculator.
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STEP 1 - Write the maths problem on the board.
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STEP 2 - Draw a bar model to represent the first part of the problem. Loaves are represented by x.
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STEP 3 - Remove the 4 from the end (the price of the pack of cheese), we are left with 3x = 6.
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Step 4 - Find the value of x, divide 6 by 3.
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STEP 5 - You’ve found the answer x = 2. Always remember to put the units back in. So 1 loaf of bread costs £2.

An operation is a mathematical process. Common examples are addition (+), subtraction (-), multiplication (x) or division (÷).

An inverse operation is the opposite of the operation used in the equation.

+ is the opposite of -

- is the opposite of +

x is the opposite of ÷

÷ is the opposite of x

Let's turn the problem below into an equation.

3 loaves of bread and a £4 pack of cheese cost £10. How much is each loaf?

In this equation we want to work out the cost of one loaf of bread.

As the cost of bread is the unknown, we will represent this with a x.

We need 3 loaves of bread, so in our equation we will represent this with 3x

We know the cheese costs £4 and the total spend is £10.

So now we can write our equation:

3x + 4 = 10

When solving an equation it is important to find the value of one letter.

Let's solve the equation 3x + 4 = 10

To remove the + 4 we complete the inverse (opposite) operation by subtracting the 4.
3x = 10 – 4
That gives us 3x = 6 (3 loaves cost £6)
To work out the cost of one loaf we divide both sides of the equation by 3.
x = 6 ÷ 3
So x = 2 (one loaf costs £2)

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