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Substitution

Replace each letter with a given number, then work out the value of the expression.

What Is Substitution?

Substitution is where algebra meets ordinary arithmetic. Once every letter has a number, BODMAS takes over. A very common mistake is forgetting that a letter next to a number means multiplication. 2 x means 2 \times x, always.

Example 1 — easy numbers

If x = 4, find the value of 3 x + 2 . 1 Replace x with 4 : 3 \times 4 + 2 2 Multiply first: 3 \times 4 = 12 3 Add: 12 + 2 = 14 Answer: 14

Example 2 — negative value

If x = - 2, find the value of 5 x + 6 . 1 Replace x with - 2 : 5 \times (- 2) + 6 2 Multiply first: 5 \times (- 2) = - 10 3 Add: - 10 + 6 = - 4 Answer: - 4

Example 3 — a squared letter

If x = 3, find the value of 2 x^{2} + 1 . 1 Replace x with 3 : 2 \times 3^{2} + 1 2 Powers before multiplication: 3^{2} = 9 3 Multiply: 2 \times 9 = 18 4 Add: 18 + 1 = 19 Answer: 19

Example 4 — two letters

If a = 5 and b = - 3, find the value of 2 a + 3 b . 1 Replace the letters: 2 \times 5 + 3 \times (- 3) 2 Multiply first: 2 \times 5 = 10, and 3 \times (- 3) = - 9 3 Add: 10 + (- 9) = 1 Answer: 1

Practice

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If x = - 4, what is x^{2} ?

If x = 5, find the value of 3 x^{2} - 4 x .

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