⚖️ Balance Lab

Every equation is a scale. Keep it level, and the answer reveals itself.

REMEMBER: An equation is a balanced scale — whatever you do to one side, you must do to the other. To solve px + q = r, undo the adding first, then the multiplying. And if you divide an inequality by a negative, the symbol flips.

Part 1 · Keep the Scale Level

Green boxes are mystery weights (x). Gold coins weigh 1 each. Both pans weigh the same — that's what the = sign promises. Use the buttons to make legal moves (same move, both sides) until one x stands alone. Or press the ⚠️ button to see what happens when you cheat...

Pick an equation

Part 2 · Graph It Right

An inequality has a whole CROWD of answers, and the number line shows them all. Read the inequality (watch out — some need a divide-by-a-negative first!). Choose your circle and your arrow, then Lock It In before the reveal.

1. The circle at the boundary number:

2. The arrow (which numbers work):

Correct graphs: 0

Part 3 · The Two-Step Solver

Build any two-step equation or inequality: px + q compared to r. The solver shows every legal move, checks its answer, runs an estimation sanity check — and graphs the solution when it's an inequality. Try a negative p with an inequality to see the famous flip!

p (with x)

q (added number)

compared to

r (other side)

Part 4 · Balance Master Quiz

Question 1 of 10 Score: 0

📗 Word Box

Equation: A math sentence with an equals sign. It promises both sides have the same value — like a level scale.
Inequality: A math sentence with <, >, ≤, or ≥. Instead of one answer, it has a whole set of answers.
Solution set: ALL the numbers that make an inequality true. We show it as a shaded ray on a number line.
Inverse operations: Operations that undo each other: adding undoes subtracting; multiplying undoes dividing.
Isolate the variable: Get x alone on one side of the scale. That's the whole goal of solving.
Open circle ○: Marks a boundary number that is NOT included (used for < and >).
Closed circle ●: Marks a boundary number that IS included (used for ≤ and ≥).
Estimate: A quick rounded calculation to check if your exact answer makes sense. Your math's smoke alarm!

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