The hardest math sprint on the site. Twenty linear equations, one at a time, drawn from four shapes: big two-steps like 9x + 47 = 137, brackets with subtraction like 5(x − 8) = 45, division forms like x ÷ 7 − 4 = 9, and the tier's signature — x on both sides, as in "7x + 4 = 3x + 24" (x = 5).
Nothing here needs more than linear reasoning, but the both-sides shape forces a real algebraic move: collect the x-terms before you unwrap. The clock counts up, a full clear is guaranteed, and your time is the only score.
How to play
One equation at a time, in order — type the value of x; an exact match advances you instantly.
Enter is optional; a wrong submission shakes the box and clears it with no penalty beyond the seconds lost.
The timer starts on your first keystroke and counts up without limit.
Give up at any point to end the sprint and see your pace graph.
What counts in this quiz
20 equations per sprint across four hard shapes: ax + b = c, ax + b = cx + d, a(x − b) = c, and x ÷ a − b = c.
Coefficients reach 12, constants reach 80, and x can exceed 200 in the division shape — but every solution is a positive whole number.
The both-sides shape is built so the x-coefficient stays positive when collected, keeping every solve clean.
What's not included — and why
No quadratics, no systems, no fractions-as-answers — every equation is linear in a single x with an integer solution, because this is a speed drill, not an exam.
Good to know
The word "equation" comes from the Latin aequare — "to make level" — the same balancing image the solving method still uses.
Diophantus of Alexandria, often called the father of algebra, wrote the unknown as arithmos — simply "the number" — some 1,400 years before x took over.
With x on both sides, subtracting the smaller x-term first is almost always the fastest route — it turns the tier's hardest shape back into a Medium problem.