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Objective The student will be able to: solve inequalities using multiplication and division. SOL: A.1, A.3 Designed by Skip Tyler, Varina High School

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What happens to the inequality symbol when you multiply each side by a positive number? The original inequality: 4 > 1 4*3 _____ 1*3 4*2 _____ 1*2 4*1 _____ 1*1

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What happens to the inequality symbol when you multiply each side by a negative number? The original inequality: 4 > 1 4*(-3) _____ 1*(-3) 4*(-2) _____ 1*(-2) 4*(-1) _____ 1*(-1)

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Here’s why it works! Multiplying or dividing each side of an inequality by a negative number changes the meaning of the inequality. You need to reverse the inequality symbol to make the inequality true. Here is an example: The original inequality: 3 > 1 3*(-2) _____ 1*(-2) (-6) _____ (-2) (-6), to < a

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Summary of Solving Inequalities with Multiplication and Division When multiplying or dividing by a negative number, usually (-1), you will change the original inequality to the opposite in order to make the inequality true!

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o -4-3-5 o -4-3-5 ● -4-3-5 -4-3-5 ● 1. 2. 3. 4. Answer Now 1) Which graph represents the correct answer to > 1

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1) Solve > 13 o -52-51-53 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

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

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2) Solve < -10 o -30-29-31 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

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

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3) Solve o -24-23-25 a > -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

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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?

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4) Solve -8p ≥ -96 1.p ≥ 12 2.p ≥ -12 3.p ≤ 12 4.p ≤ -12 Answer Now

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4) Solve -8p ≥ -96 1.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 ≤ 12 -8(12) = -96 ● 121311

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o -15-14-16 o -15-14-16 ● -15-14-16 -15-14-15 ● 1. 2. 3. 4. Answer Now 5) Solve 7v < -105

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