Math 1 · Lesson 7

Absolute Value Inequalities: Distance From Zero

Absolute value bars ask how far something is from zero. Less than a distance means between, and the word is and. Greater than a distance means outside, and the word is or. Either way you set up two problems, solve both with the Lesson 6 rules, and get two answers joined by the right word.

About 35 minutes Two problems, two answers, one word

The big idea

Absolute value is distance from zero, and a distance can be reached in two directions. That is the whole reason one absolute value sentence turns into two ordinary ones. Less than a distance keeps the inside close to zero, trapped between the two boundaries, so both facts must hold and the word is and. Greater than a distance pushes the inside far from zero on one side or the other, so only one fact can hold and the word is or. Free the bars first, read the sign, pick the word, write the two problems with the same inside, and solve both exactly the way Lesson 6 taught, flips included. Then say the answer with its word, draw it, and check a number from every piece and every gap.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Absolute value means distance from zeroThe two bars around a number ask one question: how far is this from zero? 3Less than means between: the word is andSay |inside| < 5. 4Greater than means outside: the word is orNow say |inside| > 5. 5The steps1 Rewrite Step 1 as always, inside the bars and outside them: subtraction becomes adding the additive... 6Three worked examples, every line namedOne and-example, one or-example, and one where the bars have to be freed first. 7Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the distance picture, the and/or rule with both number lines, the steps, the words we use, a fully worked example, and the traps.

Study guide (PDF)

Where this goes next

Previous lesson: Solving Inequalities: Gator Eats GreaterThe rules both of this lesson's problems are solved with, including the flip. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.