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6.2 Solving Inequalities with Mult. and Div.

This lesson explores solving inequalities using multiplication and division. Topics include whether the inequality switches when multiplying or dividing by a negative value, and examples of solving inequalities and graphing solutions.

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6.2 Solving Inequalities with Mult. and Div.

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  1. 6.2 Solving Inequalitieswith 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

  2. 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?

  3. 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?

  4. 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 ________

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

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

  7. YES !

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

  9. o -31 -30 -29 1) Solve < -10 • Draw “the river” • Clear the fraction - Multiply both sides by 3. Do you switch the inequality? • No - Both sides are being multiplied by a positive number • Simplify • Check your answer • Graph the solution {x | x < -30}

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

  11. o -53 -52 -51 2) Solve > 13 • Draw “the river” • Clear the fraction - Multiply both sides by -4 • NEW STEP!! When multiplying BOTH sides by a NEGATIVE number, SWITCH the inequality! • Simplify • Check your answer • Graph the solution { k | k < -52}

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

  13. o -25 -24 -23 3) Solve • Draw “the river” • Clear the fraction - Multiply both sides by -4. Do you switch the inequality? Yes - Both sides are being multiplied by a negative number • Simplify • Check your answer • Graph the solution {x | x > -24}

  14. 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?

  15. Answer Now 4) Solve -8p ≥ -96 • p ≥ 12 • p ≥ -12 • p ≤ 12 • p ≤ -12

  16. ● 11 12 13 4) Solve -8p ≥ -96 • Draw “the river” • Divide both sides by -8. Do you switch the inequality? Yes - Both sides are being divided by a negative number • Simplify • Check your answer • Graph the solution {p |p ≤ 12} -8(12) = -96

  17. o -16 -15 -14 o -16 -15 -14 ● -16 -15 -14 -15 -15 -14 Answer Now 5) Solve 7v < -105 ●

  18. Assignment • Page 305 13-33 odds and 46-49 all

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