Solving One-Step Equations

In a Nutshell

An equation is a balance — do the same thing to both sides and the unknown reveals itself.

An equation says two things are equal. To solve it, you find the value of the unknown that makes the equation true.

A one-step equation needs just one inverse operation to isolate the variable. Use the opposite operation to undo what has been done to the letter:

  • If the equation adds, subtract from both sides.
  • If the equation subtracts, add to both sides.
  • If the equation multiplies, divide both sides.
  • If the equation divides, multiply both sides.
x+7=12⇒x=12−7=5x + 7 = 12 \quad \Rightarrow \quad x = 12 - 7 = 5
Balance scale equation A balance scale showing x + 7 = 12. Both sides are equal. x + 7 12 = Perform the same operation on both sides to solve.

The balance scale shows that both sides must stay equal. Try subtracting 7 from both sides to solve for xx.

Watch it work

Question: Solve 3x=183x = 18.

Question 2: Solve y−9=4y - 9 = 4.

Have a go

Q1. Solve x+5=11x + 5 = 11.

Q2. Solve 4x=284x = 28.

Q3. Solve x3=5\dfrac{x}{3} = 5.

Q4. Solve n−12=3n - 12 = 3.