Two-Step Equations: 2x + 3 = 11

A7Two-Step Equations

Two undos, in the right order.

Two-step equations need two inverses — undo the add/subtract first.

Solve 2x + 3 = 11.

2x + 3 = 11

− 3 both sides → 2x = 8

÷ 2 both sides → x = 4

Think of it as a function machine: x → ×2 → +3 → 11. Undo backwards: −3, then ÷2.

Learn the 3-Step Method

1Undo the add or subtract first.

2x + 3 = 11 → subtract 3 → 2x = 8.

2x = 8

2Then undo the multiply or divide.

2x = 8 → divide by 2 → x = 4.

x = 4

3Check by substituting.

2 × 4 + 3 = 8 + 3 = 11 ✓

11 ✓

💡 Key IdeaIt's the function machine in reverse: the machine did ×2 THEN +3, so you undo +3 first, ×2 second.

Worked Example

Solve 3x − 5 = 16.

Undo −5

3x = 16 + 5 = 21

→

Undo ×3

x = 21 ÷ 3 = 7

→

✓ Check

3 × 7 − 5 = 16 ✓

x = 7

Watch Out! Common Mistakes

Dividing before subtracting.

2x + 3 = 11 → x + 3 = 5.5 ✕

Order! Undo the +3 first: 2x = 8, then x = 4. (Dividing everything by 2 works too — but then the 3 must become 1.5, which is harder.)

Sign slip when moving the number.

3x − 5 = 16 → 3x = 16 − 5 = 11 ✕

Inverse! Undo −5 by ADDING 5: 3x = 21, x = 7.

Skipping the check.

Ten seconds! Substitute back: wrong answers almost always fail the check instantly — better to know before moving on.

⬇ Cheat Sheet

TWO-STEP EQUATIONS

Undo + or − first (both sides).
Then undo × or ÷ (both sides).
It's the reverse of the function machine.
Substitute back to check.

Examples: 2x+3=11 → x=4 · 3x−5=16 → x=7.

📖 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

→

Next Lesson: A8 SequencesSpot the rule, continue the pattern.

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

Quick summary

Undo the add/subtract first, then the multiply/divide — both sides each time.
2x + 3 = 11 → 2x = 8 → x = 4.
It mirrors the function machine: last operation, first undone.
Check every solution by substituting back.

Frequently asked questions

How do you solve 2x + 3 = 11?

Subtract 3 from both sides (2x = 8), then divide both sides by 2 (x = 4). Check: 2 × 4 + 3 = 11 ✓.

Why undo the addition before the multiplication?

Because the expression was built as ×2 then +3 — undoing must reverse that order, exactly like a function machine run backwards.

Are two-step equations on the primary curriculum?

They sit at the edge of Year 6 and are common in 11+ and independent-school papers — a natural stretch after one-step equations.

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A6 One-Step Equations