Solving Two-Step Equations

Same balance scale, just one more move.

▶ Practice this concept

🧱 See It

Two mystery bags plus 3 loose blocks sit on the left. 11 loose blocks sit on the right. The scale is balanced.

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2 mystery bags + 3 blocks = 11 blocks. Each bag weighs the same amount.

✏️ Draw It

Move 1: Remove 3 blocks from both sides — exactly like a one-step equation.

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Move 2: Now 2 bags = 8 blocks. Split both sides evenly in half to find one bag.

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One bag weighs 4.

🔢 Write It

2x + 3 = 11

Move 1 — undo the addition (subtract 3 from both sides):

2x = 8

Move 2 — undo the multiplication (divide both sides by 2):

x = 4

Undo addition/subtraction FIRST, then undo multiplication/division — the reverse order of how the equation was built.

💡 Worked Examples

Example 1: 3x + 4 = 19

  1. Subtract 4 from both sides: 3x = 15
  2. Divide both sides by 3: x = 5

Example 2: 5x − 2 = 18

  1. Add 2 to both sides: 5x = 20
  2. Divide both sides by 5: x = 4

🧠 Quick Reference

Two-step equations always undo in this order: (1) addition or subtraction first, (2) multiplication or division second. Do it in the other order and the scale won't stay fair.
👪 For Parents & Tutors

BC Curriculum (Level 2 / Grade 7, Patterns & Relations): "Two-step equations with whole-number coefficients, constants, and solutions."

Why this method: Same balance-scale/algebra-tile model as Level 1's one-step equations — deliberately unchanged, since introducing a new visual model at the same time as a new algebra skill doubles the working-memory load for no benefit.

Watch for: The two-step order is the reverse of how the equation was built (it was built as "multiply, then add"; it's undone as "subtract, then divide") — this mirrors Order of Operations in reverse, which is worth pointing out explicitly if he's already solid on that Level 1 page. Losing track of *which* undo step comes first under working-memory load is the main failure mode here, not the arithmetic itself.

Comes up again: Level 3 (Grade 8) extends this to integer coefficients/constants, and Level 4 (Grade 9) adds distribution and variables on both sides — same two moves, just more of them chained together.