Substitution: Evaluate 3n + 2 (Year 6)

A4Substitution

Swap the letter for its number.

Substitution replaces the letter with a value, then calculates.

If n = 4, what is 3n + 2?

3n + 2 → 3 × 4 + 2

12 + 2 = 14

Multiply before adding — the order of operations still rules.

Learn the 3-Step Method

1Write the expression out.

3n + 2 with n = 4 becomes 3 × 4 + 2.

3 × 4 + 2

2Multiply and divide first.

3 × 4 = 12 before any adding.

12 + 2

3Then add and subtract.

12 + 2 = 14.

💡 Key Idea3n means 3 × n, so with n = 4 it's 12 — never 34. Gluing digits together is the classic substitution error.

Worked Example

If a = 5 and b = 2, find the value of 2a + 3b.

Substitute

2 × 5 + 3 × 2

→

Multiply

10 + 6

→

✓ Answer

Watch Out! Common Mistakes

Gluing the digits.

n = 4: 3n = 34 ✕

Wrong! 3n means 3 × n = 3 × 4 = 12.

Adding before multiplying.

3 × 4 + 2 = 3 × 6 = 18 ✕

Order of operations! Multiply first: 12 + 2 = 14.

Mixing up the letters.

a = 5, b = 2: 2a + 3b = 2×2 + 3×5 = 19 ✕

Match carefully! a gets 5, b gets 2: 10 + 6 = 16.

⬇ Cheat Sheet

SUBSTITUTION

Replace each letter with its value.
3n with n = 4 → 3 × 4 (never 34).
Multiply/divide before add/subtract.
Two letters? Match each to its own value.

Examples: n=4: 3n+2 = 14 · a=5, b=2: 2a+3b = 16.

📖 Continue Your Journey

✓ A1 What Is Algebra?✓ A2 Function Machines ✓ A3 Writing Expressions A4 Substitution A5 Simplifying Expressions A6 One-Step Equations A7 Two-Step Equations A8 Sequences A9 The nth Term A10 Formulae A11 Bar Models for Unknowns A12 Algebra Problem Solving

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Next Lesson: A5 Simplifying ExpressionsCollect the matching letters.

📄 Free printable: Download the Substitution cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Replace the letter with its value, keeping the hidden × visible: 3n → 3 × 4.
Order of operations applies: multiply before adding.
3n + 2 with n = 4 gives 14.
With several letters, match each to its own value carefully.

Frequently asked questions

What is substitution in algebra?

Replacing each letter with its given value and working out the result: 3n + 2 with n = 4 becomes 3 × 4 + 2 = 14.

Why isn't 3n with n = 4 equal to 34?

Because 3n means 3 multiplied by n, not the digits 3 and 4 side by side. The hidden multiplication sign must be restored when substituting.

Does BODMAS apply in algebra?

Yes — after substituting, multiply and divide before adding and subtracting, exactly as in arithmetic.

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