Solve equations with variables on both sides using balancing method. Grade 9 Alberta mathematics.
Lesson 6.2 of Linear Equations & Inequalities in Grade 9 Math — Alberta curriculum lessons.
Concept of Balance. Think of an equation like a balance scale.
Both sides must weigh the same (be equal).
If you add, subtract, multiply, or divide something on one side, you must do the exact same thing to the other side — or it becomes unbalanced.
To solve, we need to get the variable on one side of the equal sign and the constant term on the other.
Example: Keeping Balance. If we start with x + 3 = 7
Subtracting 3 from both sides keeps the equation balanced:
x + 3 - 3 = 7 - 3
Simplify x = 4
This is the Balance Strategy — maintaining equality on both sides.
The balance method helps us isolate the variable — get the unknown (like x) by itself.
This method works for all equations, even when variables appear on both sides.
Key Rules to Remember.
Understanding Variables on Both Sides. When variables are on both sides of an equation, your goal is to get all the variables on one side and numbers on the other side.
This keeps the equation balanced and allows you to isolate the variable.
Example Equation. 6x + 2 = 10 + 4x
To solve, you'll use the same balance strategy — whatever you do to one side, you must do to the other — but now you'll have to move terms from one side to the other.
Solve: x + 12 = 20
Step 1: Identify What's Being Done to x. 12 is added to x
Step 2: Use the Inverse Operation to Keep Balance. Subtract 12 from both sides
Step 3: Apply it Equally to Both Sides. (x + 12) - 12 = 20 - 12
Step 4: Simplify. x = 8
Step 5: Check the Solution. 8 + 12 = 20 ✅
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