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Mastering Inequalities: Multiplying and Dividing Techniques

This lesson focuses on solving inequalities through multiplication and division, emphasizing the importance of understanding positive and negative numbers. Students will learn how to determine when to reverse the inequality sign, ensuring they apply the correct properties when manipulating inequalities. The materials include step-by-step examples, practice problems, and graphical representations of solutions to enhance comprehension. By the end of the lesson, students should be confident in their ability to solve inequalities and understand the underlying principles.

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Mastering Inequalities: Multiplying and Dividing Techniques

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  1. Bell RingerSolve c – 2 > 20 Go over homework

  2. 6-6 Solving Inequalities by Multiplying or DividingObjectiveThe student will be able to: solve inequalities using multiplication and division.

  3. POSITIVE NUMBERS ONLYMultiplication & Division properties of inequalities You can multiply or divide the same positive number or positive term on each side of the inequality, the relationship between the two sides does not change. 8p ≥ -96 < -10 ≥ The inequality stays the same

  4. NEGATIVE NUMBERS ONLYMultiplication & Division properties of inequalities When multiplying or dividing the same negative number or negative term on each side of the inequality, you must reverse the inequality sign -8p ≥ -96 > -10 ≤ < -3 The inequality gets flipped every time you * or / by a negative number

  5. To solve for a variable the variable must be positive with no number beside it!!  x = 10 Solved - x = -5 Not solved 2x = 5 Not solved -3x =6 Not solved

  6. o -53 -52 -51 1) 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 < -52

  7. Answer Now 2) When solving < -10will the inequality switch? • Yes! • No! • I still don’t know!

  8. o -31 -30 -29 • 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 2) Solve < -10 x < -30

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

  10. 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 a > -24

  11. ● 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 ≤ 12 -8(12) = -96

  12. o -5 -4 -3 o -5 -4 -3 ● -5 -4 -3 -5 -4 -3 Answer Now 1) Which graph represents the correct answer to > 1 Multiply both sides by -4 Switch inequality sign K < -4 ●

  13. o -16 -15 -14 o -16 -15 -14 ● -16 -15 -14 -15 -15 -14 Answer Now 5) Solve 7v < -105 Divide both sides by 7 V < -15 ●

  14. HW - > page 291 #6-22 even 6-12 show work (2 pts each) 14-20 show work and graph solution (3pts each)

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