Math 1 · Lesson 6

Solving Inequalities: Gator Eats Greater

An inequality is an equation with a hungry sign in the middle. You solve it with the same three steps as Lesson 5, and you can name the property on every line. There is exactly one new rule: multiply both sides by a negative number, and the gator turns around.

About 30 minutes One new rule, and a number line to see why

The big idea

An inequality is solved with the very same moves as an equation: rewrite into plus and times, distribute and combine, add opposites to both sides, then multiply by the reciprocal. Every line still has a property name. The only difference is that the sign in the middle is a gator, and a gator cares which side is bigger. Adding the same thing to both sides never changes which side is bigger. Multiplying both sides by a positive number never changes it either. Multiplying by a negative number is taking opposites, and opposites mirror the number line, so the bigger side becomes the smaller side and the gator has to turn around. That is why the flip happens exactly once, at the very last step, and only when the coefficient (the number on the variable) is negative. Check three numbers and the check will tell you if you forgot.

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 2Gator eats greaterThe sign in the middle of an inequality is a gator's open mouth, and the gator is always hungry for the... 3Why the gator turns aroundTake the sentence x < 5 : x is somewhere to the left of 5. 4The three steps, one rule addedSolve an inequality exactly the way Lesson 5 solved an equation. 5Three worked examples, every line namedThe number you add to both sides or multiply both sides by is shown in this color . 6Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the gator, the flip rule and why it works, the three steps, the words we use, a fully worked example with every property named, and the traps to watch for.

Study guide (PDF)

Where this goes next

Previous lesson: Longer Equations: Combine, Then SolveThe three steps this lesson borrows, with every property named. Next lesson: Absolute Value InequalitiesDistance from zero, two problems, and the word between the answers: and, or or. 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.