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NEXUS

- EDEXCEL GCSE
- AQA GCSE
- OCR GCSE
- EDUQAS GCSE

Algebra follows the same rules you have used with numbers, but because the number is unknown it can look very different.

If we do not know the value of a number, we can call it \( x \), \( a \) or whichever letter we like.

\[3 \times 5 = 15 \]

If we multiply two numbers, such as 3 and 5, we can write the answer.

\[3 \times x \]

We cannot do this with algebra because we do not know what the number is.

\[3 \times x = 3x \]

The \(\times \) and the \( x \) look very similar! Thankfully we never have to show the (\times \) sign in algebra.

\[3 \times x + 10 = 3x + 10 \]

If we added 10 to \( 3x \) we can write this as \( 3x + 10\)

If we find out what number the letter represents, we can find the value of an expression by using substitution.

\[ 3x + 10\]

If \( x = 4 \) we can find the value of \( 3x + 10 \) by replacing the x for 4. But be careful! We must first put back in the times sign.

\[ 3 \times x + 10\]

\[ 3 \times 4 + 10\]

\[ 12 + 10\]

\[ 22\]

An equation is where we have two expressions equal to each other. You can spot an equation because it will have an equals sign.

\[ 3x + 5 = 14\]

In this equation, x is a value that can be found.

A formula is a statement linking more than one variable (can be real-world).

\[ A = \frac12 \times b \times h\]

You might recognise this formula as the area of a triangle. Each letter means something. \(b\) is the base of the triangle and \(h\) is the height.

An identity is a statement that is true for all values of the variable.

\[ 3x = x + x + x\]

This identity is true for all values of \(x\).

\[3 \times 5 = 5 + 5 + 5\]

\[3 \times 10 = 10 + 10 + 10\]

\[3 \times 999 = 999 + 999 + 999\]

We can show identities with three equals signs (but they will probably use two in your exam).

\[ 3x \equiv x + x + x\]

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