Modeling with inequalities

Real life rarely has exact numbers. We have caps, minimums and budgets — perfect for inequalities.

Examples

• "You can spend at most $50" → x ≤ 50.
• "Score at least 1200 to qualify" → s ≥ 1200.
• "Capacity is fewer than 30" → p < 30.

Worked example

A streaming app costs $3 per month plus $1 per movie rental. Mia's monthly budget is $15.

3 + 1 · m ≤ 15
m ≤ 12

So Mia can rent up to 12 movies per month.