Algebra
Solving linear equations
Keep equality while undoing operations.
Predict, test and explain
Step 1 of 3
Predict
In 3x + 2 = x + 10, what should happen when +2 moves from the left side to the right?
Drag a highlighted card across =, or tap it. Arrow keys also move cards.
Move a whole signed term across the equals sign.
Moving an additive term applies the opposite operation to both sides. Move its sign and coefficient with it. A multiplier can divide both sides only after the x-terms and constants are separated.
Check the working
| Quantity | Equation |
|---|---|
| Original | |
| Current | |
| Collected terms |
Explore and compare
Choose the investigation above. Predict what will change before you move a control.
Try it in the simulation. Change one thing at a time.
Notes and saved values stay in this tab. They disappear when you reload.
Hints, self-check and connections
Try a self-check
Fixed values, separate from the diagram controls.
Solve this equation.
Hint
Subtract the variable term on the right from both sides, then undo the remaining operations.
Reveal answer
Subtract twice the variable and add five on both sides, then divide by two.
Build an explanation
Hint 1
Keep both whole sides equal. Adding or subtracting the same quantity on both sides preserves the solutions.
Hint 2
To move an additive term, apply its additive inverse to both sides. Treat −4 as the whole signed term: removing it means adding 4 to both sides.
Hint 3
After collecting terms, undo a non-zero coefficient by dividing both whole sides by it. Multiplication or division preserves equivalence only when the multiplier or divisor is non-zero.
Worked example
This example uses fixed values, separate from the diagram controls.
Solve 3x − 4 = x + 8.
- Subtract x from both sides: 2x − 4 = 8.
- Add 4 to both sides to cancel the complete term −4: 2x = 12.
- Divide both sides by the non-zero coefficient 2: x = 6.
- Check in the original equation: 3 × 6 − 4 = 14 and 6 + 8 = 14.
Answer: x = 6.
Connect this idea
Watch out: Additive terms and factors need different inverse operations. You subtract a term but divide by a non-zero factor; dividing by zero is undefined, and multiplying by zero loses information.