Solving linear inequalities
A condition says “at most” or “more than” instead of “equals”. How do you find every number that passes, and when does the sign turn around?
Where you are 3 inside
What this area is about
A linear inequality such as 3x + 5 \le 26 is usually true for a whole stretch of numbers, not one. Solving it uses the same moves as solving an equation, with one exception: multiplying or dividing both sides by a negative number reverses the inequality sign. Every step must leave the solution set exactly as it was.
How these fit together
All three children are procedures, each building on the one before.
One-step inequalities and the sign flip sets out what a solution set is, which moves keep it, and why the sign flips: -2x < 6 becomes x > -3.
Two-step inequalities undo two operations in reverse order, as in px + q > r with p \ne 0, watching for a negative p.
Multi-step inequalities clear parentheses, collect the unknown from both sides, then solve, flipping the sign whenever both sides are multiplied or divided by a negative number.
A path through it
One-step inequalities, then two-step, then multi-step: each lesson leans on the one before.
Next: compound inequalities, modeling constraints with inequalities and systems of inequalities.