Same Math › Grades 7–8 › The balance method
What is the balance method for equations?
The balance method treats an equation like a balanced scale: whatever you do to one side, you do to the other, so it stays balanced. To solve 3x + 4 = 19, take 4 from both sides (3x = 15), then divide both sides by 3 (x = 5).
- Left side and right side weigh the same.
- Undo the operations, one step at a time, on both sides.
- Check: 3 × 5 + 4 = 19.
Why schools teach it
It replaces “move it to the other side”
Seventh graders solve equations like 3x + 4 = 19 (7.EE.B.4a), and eighth graders solve equations with x on both sides (8.EE.C.7). Many of us learned to “move the 4 over and change its sign,” which works but hides why.
The balance picture explains it: subtracting 4 from both sides keeps them equal. Kids who understand that don't lose track of signs when equations get longer.
At the kitchen table
What to say, and what to skip
Say this
What's being done to x?
Times 3, plus 4.What undoes that? Do it to both sides.
Is it still balanced?
Plug your answer back in. Does it work?
Checking is part of solving.
Skip this
Move the 4 to the other side and flip the sign.
It works, but say “subtract 4 from both sides” so the reason is clear.- Guess and check only.Fine for a start; the method works when guessing doesn't.
- Skipping the check.Substituting the answer catches most mistakes.
See it in action
Solving 5x + 2 = 3x + 10
Subtract 3x from both sides
2x + 2 = 10Subtract 2 from both sides
2x = 8Divide both sides by 2, then check
x = 4: 5(4) + 2 = 22 = 3(4) + 10
Writing each step under the last, lined up at the equals sign, keeps work tidy.
Free practice sheet
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Parents also ask
What's a hanger diagram?
A picture of a balanced mobile with shapes on each side. It's often used before writing equations.
Why undo in reverse order?
To get x alone, peel away the last thing done to it first, like unwrapping a present.
What if x is on both sides?
Get all the x terms on one side first by subtracting from both sides.
Is this the same as inverse operations?
Yes. Addition undoes subtraction; division undoes multiplication.