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Algebraic Expressions & Substitution
Rung 2 of 4 · The method

Substitute, Then Evaluate

Every "evaluate the expression" question is the same two moves. Get them automatic and the marks look after themselves.


PractiseHit “new expression”, work it out, then check yourself. Peek at the steps if you’re stuck.
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"Evaluate by substitution" sounds fancy, but it's two moves: swap the letter for its value, then work out the sum using the order of operations. That's the lot.

The Two Moves

One — substitute. Wherever the letter appears, write the number in its place. Keep the hidden times sign: 3a becomes 3 × (the value), not the two numbers shoved together. Brackets around the value are a tidy habit, especially once negatives turn up.

Two — evaluate. Now it's just arithmetic. Run the order of operations — brackets, then indices, then × and ÷, then + and −.

A Worked One

Evaluate 3a − 4 when a = 6. Substitute: 3 × 6 − 4. Evaluate: do the multiply first, 18 − 4 = 14. So the answer is 14. Notice the order mattered — multiply before the subtraction.

Say it plainly: write the number where the letter was (keep the × sign), then do the arithmetic in the proper order. Substitute, then evaluate.

Brackets Do Their Job

For 2(x + 5) with x = 3: substitute to get 2(3 + 5), do the bracket first, 2 × 8 = 16. The bracket tells you what to add before you multiply — the order of operations is quietly steering the whole thing.

Us, Thinking Out Loud

Could you teach me the two moves without looking?

Why does keeping the times sign in 3a matter so much?