Goal: get exactly one positive x on a tray, with only units on the other tray. The last step reads x = a number (or the same equation reversed). You must also cancel any zero pairs. Complete eight guided tasks, then keep playing randomly generated integer challenges.

Stacking: positive blocks sit on top of a plate; negative blocks attach to its underside, stacking downward. Plates stay horizontal as the beam tips, and the heavier signed total lowers its side. Use Sandbox to explore unequal loads.
Negative pieces: a +1 is a downward unit weight; a −1 is an upward antigravity unit. A +x piece applies x units of downward force, and a −x piece reverses that force. If x is negative, the variable forces reverse direction: +x pushes upward and −x pushes downward. “Gravity” and “Antigravity” name the sign of the piece, not a promise that x is positive.

Zero pairs: +1 with −1, or +x with −x, has zero net effect. Subtracting adds upward pieces; use Cancel zero pairs to simplify. Multiplying by a negative factor switches the force signs. Dividing regroups the net pieces; it is allowed only when all resulting coefficients and constants are integers. Zero is never a valid factor.

Challenges: x is hidden, and the scale is evaluated at the equation’s actual solution. Valid moves keep it balanced. Balance alone is not a solution: you need to isolate x. Undo removes the last move; Restart task restores that challenge. Hints suggest one next step.

Sandbox: edit each side independently and adjust x to test the equation. The scale tilts toward the greater signed total. An equation can be true for one x, every x, or no x. All pieces use integer coefficients; large quantities are grouped and labeled. The workspace permits coefficients and constants up to 10,000 in magnitude.