One-Step Equations

Study Sheet

One-Step Equations

Undoing what was done to x

Keep the Balance

Concept
The Big Idea

An equation is a balance. Whatever you do to one side you must do to the other, and you undo an operation with its opposite.

Example
Solving 4x=284x = 28

xx was multiplied by 44, so divide both sides by 44: x=7x = 7. Check: 4×7=284 \times 7 = 28.

In Plain Terms & More Examples

Concept
In plain terms

Undo whatever was done to the letter using the opposite operation — an inverse operation — doing the same thing to both sides so the balance holds (the properties of equality).

Example
Solving x+9=15x + 9 = 15

Subtract 99 from both sides: x=6x = 6. Check: 6+9=156 + 9 = 15.

Example
Solving x3=4\dfrac{x}{3} = 4

Multiply both sides by 33: x=12x = 12. Check: 12÷3=412 \div 3 = 4.