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Lesson 3.4 Solving Two-Step and multi-step Inequalities

Lesson 3.4 Solving Two-Step and multi-step Inequalities. Objectives. Solve inequalities that contain more than one operation.

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Lesson 3.4 Solving Two-Step and multi-step Inequalities

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  1. Lesson 3.4 Solving Two-Step and multi-step Inequalities

  2. Objectives • Solve inequalities that contain more than one operation

  3. Inequalities that contain more than one operation require more than one step to solve. Use inverse operations to undo the operations in the inequality one at a time.

  4. Steps to solve a Two-step inequality Step 1: Undo addition or subtraction Step 2: Undo multiplication and division Is your variable isolated?

  5. Remember! Subtracting a number is the same as adding its opposite. 7 – 2t = 7 + (–2t)

  6. 45 + 2b > 61 –45 –45 b > 8 0 2 4 6 8 10 14 20 12 18 16 Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 45 + 2b > 61 1. Add/ Subtract 2. Multiply/Divide 2b > 16 The solution set is {b:b > 8}.

  7. 8 – 3y ≥ 29 –8 –8 –7 –8 –10 –6 –4 0 2 4 6 8 10 –2 Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 1. Add/Subtract 8 – 3y ≥ 29 2. Multiply/Divide –3y ≥21 The solution set is {y:y  –7}. y≤ –7

  8. You try Solve and Graph the inequality

  9. To solve more complicated inequalities, you may first need to simplify the expressions on one or both sides.

  10. 10 –8 –10 –6 –4 0 2 4 6 8 –2 –3 Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. 2 – (–10) > –4t 1. Combine like terms. 12 > –4t 2. Multiply/Divide –3 < t (or t > –3) The solution set is {t:t > –3}.

  11. –8 + 4x ≤ 8 +8 +8 –8 –10 –6 –4 0 2 4 6 8 –2 10 Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. –4(2 – x) ≤ 8 1. Distributive Property −4(2 – x) ≤ 8 −4(2) − 4(−x) ≤ 8 2. Add/Subtract 3. Multiply/Divide 4x ≤16 x ≤ 4 The solution set is {x:x ≤ 4}.

  12. Now you try… 1. 3x – 7 > 2 4. x – 4 < 3 5 2. 4x + 1  -3 5. 15 + x ≥ 6 3 3. 2x – 7 ≤ -3 x > 3 x < 35 x ≥ -1 x ≥ -27 x ≤ 2

  13. Lesson Quiz: Part I Solve each inequality and graph the solutions. 1. 13 – 2x ≥ 21 x ≤–4 2. –11 + 2 < 3p p >–3 t > 7 3. 23 < –2(3 – t) 4.

  14. Lesson Quiz: Part II 5. A video store has two movie rental plans. Plan A includes a $25 membership fee plus $1.25 for each movie rental. Plan B costs $40 for unlimited movie rentals. For what number of movie rentals is plan B less than plan A? more than 12 movies

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