Solve in Terms of the Parameter, Then Impose the Condition
When an equation, inequality or system carries a letter constant, solve it as if that letter were a number: the solution comes out as an expression in it. The extra demand -- a natural-number solution, both solutions positive, exactly three whole numbers in range, a fraction in lowest terms -- then becomes a condition on the parameter, and that is what you solve. Usually the solving is ordinary; only the filter is new.
grade 7–8 Expressions Convert to AlgebraEliminate Possibilities
Progression (5)
g7 1. Write the solution in a, then filter by wholeness Expressions
g7 2. Pin the boundary so exactly three naturals fit Expressions
g8 3. Solve in terms of a, then demand positivity Expressions
g8 4. Write the solution in terms of the constant Expressions
g7 5. Equation fixes the form, inequality bounds it ExpressionsNumber system