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

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

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)

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

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!

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

1) Solve > 13 o k < 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

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

2) Solve < -10 o x < 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

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

3) Solve o a > 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 ≤ 12 -8(12) = -96 ●

o o ● ● Answer Now 5) Solve 7v < -105