Using Multiplication & Division Solving Inequalities Using Multiplication & Division

Think about this inequality: If it were an equation, you would know how to solve it.

Multiply both sides by 1/3.

Could you just do the same thing for an inequality?

Is the solution true? Solution: Means that all numbers less than 9 should be true. Substitute some of those numbers into the inequality to test : √ √ √

Will all numbers less than 9 make the sentence true? As x gets smaller, 3x gets smaller and is definitely less than 27. But what about negative numbers? √ √ √ Negative numbers are always less than positive numbers!

So…we solve this inequality as we did with equations: √

Try this one: ?

Is the solution true? Solution: Means that all numbers less than -9 should be true. Substitute some of those numbers into the inequality to test : NO!

New Rule! If you multiply both sides of an equation by a negative number, you must FLIP the inequality symbol!

Solve again: >

Is the solution true? Solution: Test numbers greater than 9: What numbers are greater than -9? 5 10 15 -20 -15 -10 -5 -25 20 25 -9

√ √ √

Solve each inequality:

Answers: