MISSION · Algebra
Solving Linear Equations
Isolate the unknown without losing the equality
LEVEL 1 · EXPLORE
Make the idea move
Change the controls and watch what happens. Follow your curiosity and see what you notice.
Loading the activity…
LEVEL 2 · LEARN
Unlock the explanation
Open the chapters in any order. Try the examples as you go.
The idea in one sentence
An equation is a balanced scale, so whatever you do to one side must also happen to the other.
Undo operations in reverse
Solve \(3x + 5 = 20\) by undoing what happened to \(x\):
- Subtract 5 from both sides: \(3x = 15\).
- Divide both sides by 3: \(x = 5\).
The order matters. The expression says “multiply by 3, then add 5,” so solving walks backward: subtract 5, then divide by 3.
Check the answer
Replace \(x\) in the original equation:
\[3(5) + 5 = 15 + 5 = 20\]The left side becomes the right side, so \(x = 5\) works.
Variables on both sides
For \(5x - 2 = 2x + 10\), gather the variable terms on one side:
\(5x - 2 = 2x + 10\) \(3x - 2 = 10\) \(3x = 12\) \(x = 4\)
Each line keeps the scale balanced.
Common mix-ups
- Moving a term and changing its sign without understanding why. Instead, name the same operation on both sides.
- Dividing only one term. In \(3x + 6 = 12\), subtract 6 first or divide every term by 3.
- Stopping without checking. Substitution catches sign mistakes fast.
Check yourself
Solve \(4x - 7 = 13\), then substitute your answer into the original equation.
\(4x = 20\), so \(x = 5\). Check: \(4(5) - 7 = 13\).
LEVEL 3 · REFLECT
Add this quest to your trail
When you feel ready, mark this idea as explored. You can always come back and try it again.
EXPLORER STRATEGIES