Equations

Ages 10–14

Difficulty adapts to you

Equations

An equation says that two things are equal. To solve it, find the value of the variable that makes the equation true. Do the same operation to both sides to keep it balanced.

Your goals

✓You can solve simple equations.
✓You can use equation, solution correctly.
✓You can substitute your solution into the original equation.

Words to know

equation:: A statement that two expressions are equal.
solution:: A value that makes an equation true.

Examples

1x + 5 = 12 → subtract 5 from both sides → x = 7
23x = 18 → divide both sides by 3 → x = 6

More than one way to solve it

Try each method, then choose the one you can explain and check most clearly.

Method 1

Inverse operations

Best for: One- and two-step equations

1.Identify what was done to the variable.
2.Undo operations in reverse order.
3.Check by substitution.

Example: 3x + 5 = 20 → 3x = 15 → x = 5.

Method 2

Balance model

Best for: Understanding why both sides stay equal

1.Picture both sides as a balanced scale.
2.Perform the same action on both sides.
3.Continue until the variable is alone.

Example: Remove 5 from both sides of 3x + 5 = 20, then divide both sides by 3.

Check these

• Do not perform an operation on only one side.
• Keep every number, symbol, label, and unit in its correct place.
• Choose the method that makes each step easiest to explain and check.

Helpful habits

• Read the whole question before choosing what to do.
• Show one clear step at a time and check each step.
• If you are stuck, draw a model, try smaller numbers, or revisit the example.

Now try your own

Create your own equations example, solve it, and explain how you checked it.

Professor Wise Owl

Wisdom & Understanding

“Every expert was once a beginner. You are on your way!”