Inequalities

Ranges instead of points.

Almost the same rules

You can add, subtract, multiply and divide both sides as with equations, with one exception: multiplying or dividing by a negative flips the direction of the sign.

The solution is a range, best drawn on a number line.
Combining inequalities with and gives an overlap, with or gives a union.

Where they matter

Constraints in real problems are almost always inequalities: budgets, capacities, tolerances. Optimisation is the study of pushing against them.