6.2 Solving Inequalities with Mult. and Div. solve inequalities using multiplication and division. PFA 7 and 9 Designed by Skip Tyler, Varina High School Edited by Eddie Judd, Crestwood Middle School Edited by Dave Wesley, Crestwood Middle School

Investigate If 5 > 2, can I multiply each side by 10 and keep the inequality true? If 5 > 2, can I multiply each side by -10 and keep the inequality true?

Investigate If 4 < 12, can I divide each side by 2 and keep the inequality true? If 4 < 12, can I divide each side by -2 and keep the inequality true?

What do we know? Multiply or divide by a ____________ will not affect the inequality. Sign ________ Multiply or divide by a ____________ will affect the inequality. Sign ________

Let’s look at this idea again! What if my original inequality contains a negative value? (multiply) For example: -5 < 10

Conclusion What if my original inequality contains a negative value? (divide) For example: 8 > -2 Do I still agree?

YES !

1) When solving > -10 will the inequality switch? 1.Yes! 2.No! 3.I still don’t know! Answer Now

1) Solve < -10 o {x | x < -30} 1.Draw “the river” 2.Clear the fraction - Multiply both sides by 3. Do you switch the inequality? No - Both sides are being multiplied by a positive number 3.Simplify 4.Check your answer 5.Graph the solution

o o ● ● Answer Now 2) Which graph represents the correct answer to > 1

2) Solve > 13 o { k | k < -52} 1.Draw “the river” 2.Clear the fraction - Multiply both sides by -4 3.NEW STEP!! When multiplying BOTH sides by a NEGATIVE number, SWITCH the inequality! 4.Simplify 5.Check your answer 6.Graph the solution

3) When solving will the inequality switch? 1.Yes! 2.No! 3.I still don’t know! Answer Now

3) Solve o {x | x > -24} 1.Draw “the river” 2.Clear the fraction - Multiply both sides by -4. Do you switch the inequality? Yes - Both sides are being multiplied by a negative number 3.Simplify 4.Check your answer 5.Graph the solution

Take a quick break! Things that make you go.....Hmmm Why is abbreviation such a long word? Why do they have braille dots on the ATM machines in drive-thru’s?

4) Solve -8p ≥ p ≥ 12 2.p ≥ p ≤ 12 4.p ≤ -12 Answer Now

4) Solve -8p ≥ Draw “the river” 2.Divide both sides by -8. Do you switch the inequality? Yes - Both sides are being divided by a negative number 3.Simplify 4.Check your answer 5.Graph the solution {p | p ≤ 12} -8(12) = -96 ●

o o ● ● Answer Now 5) Solve 7v < -105

Assignment Page odds and all