A sealed box, a tilting scale, and one legal move — solving is finding what makes it TRUE.
REMEMBER: An equation is a question: which value
makes both sides equal? A solution is a value that makes it TRUE —
test it by substituting! To solve, undo what was done to x with the
inverse operation, on BOTH sides. An inequality like x > 40 has
infinitely many solutions — but not 40 itself.
Part 1 · The Mystery Scales — Solution Tester
A sealed box 📦 of unknown weight sits on the scale. Pick a puzzle, then slide
the test value — the scale tilts toward the heavier pan, and balances ONLY at
the true solution. Every equation is a question; the scale answers true or false.
Part 2 · The Ride Gate — True or False?
Gates run on inequalities. Read the rule, look at the value at the gate, and
commit: does it get through? Then the number line reveals the
whole solution set — an endless shaded ray.
Correct gate calls: 0
Part 3 · Detective Machines
Three machines crack the cases. Each prints its steps — the legal move, the
check, and the why.
Solve x + p = q or p·x = q with ONE legal move — the inverse operation on both sides.
Turn a real-world rule into an inequality — and meet its infinite solution set.
Two quantities changing together: distance d = r·t. Choose the speed, pick a time — table, equation, and roles all connect.
Part 4 · Chief Detective Quiz
Question 1 of 10Score: 0
📗 Word Box
Equation
A statement that two expressions are equal — a balanced scale, and a question waiting for its answer.
Solution
A value that makes an equation or inequality TRUE. Test any candidate by substituting it in.
Inverse operations
Operation pairs that undo each other: + and −, × and ÷. Solving uses the inverse of whatever was done to x.
Inequality
A statement comparing with < or > instead of = — like w > 40. The scale tips instead of balancing.
Solution set
ALL the values that make a statement true. For x > 40 it's an endless ray of numbers — infinitely many.
Boundary value
The number where the ray begins (40 in x > 40). With strict < or >, the boundary itself is NOT a solution — the circle stays open.
Independent variable
The quantity you choose freely — the input, like time t in d = 65t. It goes on the horizontal axis.
Dependent variable
The quantity that responds — the output, like distance d. Its value DEPENDS on the input.