Solving Two-Step Equations

In a Nutshell

Two-step equations need two inverse operations — undo the addition or subtraction first, then the multiplication or division.

A two-step equation involves two operations applied to the variable. To solve it, you reverse the operations in the opposite order to how they were applied (just like undoing a function machine backwards).

The general approach for an equation like 3x+5=203x + 5 = 20:

  1. Undo the addition/subtraction (the term without xx).
  2. Undo the multiplication/division.
3x+5=20→−53x=15→÷3x=53x + 5 = 20 \quad \xrightarrow{-5} \quad 3x = 15 \quad \xrightarrow{\div 3} \quad x = 5
Balance scale for solving two-step equations A balance scale with bags representing x and unit squares representing numbers. Applying the same operation to both sides keeps it balanced, revealing the value of x.
Equations:

Use the controls to subtract 5 from both sides, then divide both sides by 3. Watch the equation simplify step by step.

Watch it work

Question: Solve 4x−3=174x - 3 = 17.

Question 2: Solve x2+6=10\dfrac{x}{2} + 6 = 10.

Have a go

Q1. Solve 2x+7=152x + 7 = 15.

Q2. Solve 5y−2=235y - 2 = 23.

Q3. Solve n4+3=8\dfrac{n}{4} + 3 = 8.

Q4. Solve 6x+1=496x + 1 = 49.