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Warm Up Solve each equation. 1. –5 a = 30 2.

Warm Up Solve each equation. 1. –5 a = 30 2. –10. –6. 3. 4. Graph each inequality. 5. x ≥ –10. 6. x < –3. Lesson 3.3 Solving Inequalities by Multiplying or Dividing. Less than or equal to. Less than. ≤. <. greater than. greater than or equal to. >. ≥.

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Warm Up Solve each equation. 1. –5 a = 30 2.

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  1. Warm Up Solve each equation. 1. –5a = 30 2. –10 –6 3. 4. Graph each inequality. 5. x ≥ –10 6.x < –3

  2. Lesson 3.3Solving Inequalities by Multiplying or Dividing Less than or equal to Less than ≤ < greater than greater than or equal to > ≥

  3. California Standards Preparation for 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

  4. Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly ≤ is less than or equal to ≥ is greater than or equal to Notice colored incircles

  5. Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly < is less than Notice open circles > is greater than

  6. Solving Inequalities Using Multiplication x -2 3 x -2 3 x  -6 Translation: x divided by 3 is greater than or equal to negative 2. The opposite of divided by 3 is Multiplying by 3. What you do on one side you do on the other! • 3 3 • Graph -6 -4 -2 0 4

  7. 3x ≤ 12 3x ≤ 12 3 Solving Inequalities Using Division Translation: 3times x is less than or equal to 12. The opposite of multiplying by 3 is divided by 3. What you do on one side you do on the other! 1 3 x ≤ 4 Graph -4 -2 0 2 4

  8. Solve the inequality. Then graph the solution.

  9. Multiplying and Dividing Inequalities by aNegative Number Step1: solve for m -divide by -3 Step 2: reverse the inequality symbol Solve the inequality. 12> -3m 4 < m 12 > -3m < -3 -3 When multiplying or dividing by a negative number reverse the inequality symbol.

  10. Multiplying and Dividing Inequalities by aNegative Number Solve the inequality. k < -3 Step1: solve for k -Multiply by -2 Step 2: reverse the inequality symbol -2. .-2 -2 k > 6 > When multiplying or dividing by a negative number reverse the inequality symbol.

  11. Tell whether the operation reverses the sign of the inequality. • Multiply each side by -1 • Multiply each side b 3) Divide each side by 4. 4) Divide each side by -5.

  12. You try: Solve the Inequalities

  13. number of tubes is at most times $20.00. $4.30 4.30 20.00 ≤ p • Additional Example: Application Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy? Let p represent the number of tubes of paint that Jill can buy.

  14. Additional Example Continued Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy? 4.30p ≤ 20.00 Since p is multiplied by 4.30, divide both sides by 4.30. The symbol does not change. p ≤ 4.65… Since Jill can buy only whole numbers of tubes, she can buy 0, 1, 2, 3, or 4 tubes of paint.

  15. Lesson Quiz Solve each inequality and graph the solutions. 1. 8x < –24 x < –3 2. –5x ≥30 x ≤ –6 4. 3. x > 20 x ≥ 6 5. A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible numbers of shirts she can buy? 0, 1, 2, 3, 4, 5, 6, or 7 shirts

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