Unit 8

Inequalities

One-variable, the sign-flip, compound, absolute value, two-variable graphing

This unit is about the math of "enough," "at most," and "in range." A lot of real life isn't one exact number but a whole range of values that work, and inequalities are how you write that down and reason about it. If your arithmetic with negative numbers feels a little rusty, a quick warm-up there will help, since negatives show up often.

Here's a habit worth keeping for this unit and the rest of the book. Before you start a new lesson, redo two or three problems from a lesson or two back from memory first.

It feels like a detour and it isn't. Pulling a method back from memory is a few minutes well spent, and it's a big part of why a skill is still there next week.

An inequality is an equation with a direction. Almost everything you already do to solve an equation carries straight over: isolate the variable with balanced moves.

There's exactly one new rule, and it's the source of most slips in the whole unit. So the first lesson spends its time on that rule, and on a check that catches it every time.

After that, the unit chains two conditions together, reads absolute value as plain distance, and finally lifts the whole picture into two variables, where the answer becomes a shaded region instead of a line.