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3.5 Compound Inequalities

3.5 Compound Inequalities. Objective: SWBAT solve compound inequalities. Mini Quiz 24. 1. Solve 2 x – 3 ≤ 5 x + 9 2. Solve 2 x – 4 ≤ 2(3 x – 6) 3. Is -2 a solution to the inequality x – 2 ≤ 5(x-1). Quick Review. 1. Evaluate |-4| 4 2. True or False: |-5| = -5 False

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3.5 Compound Inequalities

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  1. 3.5 Compound Inequalities Objective: SWBAT solve compound inequalities.

  2. Mini Quiz 24 1. Solve 2x – 3 ≤ 5x + 9 2. Solve 2x – 4 ≤ 2(3x – 6) 3. Is -2 a solution to the inequality x – 2 ≤ 5(x-1)

  3. Quick Review 1. Evaluate |-4| 4 2. True or False: |-5| = -5 False 3. What two values can x equal for the equation |x| = 8 -8, 8 4. What is the distance of 3 and -2? 5

  4. Compound Inequality Compound Inequality - two inequalities connected by andor or(this is similar to compound sentences in English, which are joined by and, or, or but). Example: 0 < x ≤ 4 (aka 0 < x and x ≤ 4) x < -1 or x > 2 (or can’t be combined) Note: it’s one way OR the other 0 0

  5. Compound Inequality with “OR” Solve and graph the solution 1. 3x + 1 < 4 or 2x – 5 > 7 3x < 3 or 2x > 12 x < 1 or x > 6 0

  6. Compound Inequality with “AND” Solve and Graph 2. -2 ≤ 3x – 8 ≤ 10 Method 1: Method 2: -2 ≤ 3x – 8 ≤ 10 -2 ≤ 3x – 8 and 3x – 8 ≤ 10 +8 + 8 +8 +8 + 8 +8 +8 6 ≤ 3x ≤ 18 6 ≤ 3x and 3x ≤ 18 3 3 3 3 3 3 3 2 ≤ x ≤ 6 2 ≤ x and x ≤ 6 2 ≤ x ≤ 6 0

  7. Solving Compound Inequalities with “AND” and “OR” Solve and Graph the inequalities 3. –2 < -2 – x < 1 0 > x > -3 0

  8. Solving Compound Inequalities with “AND” and “OR” Solve and Graph the inequalities 4. 2x + 3 < -1 or 3x – 5 > -2 x < -2 or x > 1 0

  9. Solving Compound Inequalities with “AND” and “OR” Solve and Graph the inequalities 5. 7 < 4 + x < 8 3 < x < 4 0

  10. Solving Compound Inequalities with “AND” and “OR” Solve and Graph the inequalities 6. -1 < 2x + 3 ≤ 13 -2 < x ≤ 5 0

  11. Solving Compound Inequalities with “AND” and “OR” 7. 4x – 1 > 7 or 5x – 1 < -6 x < 2 or x < -1 0

  12. Wrap Up Compound Inequalities • OR - solve each one separately • AND – isolate variable or break into two problems and solve each one separately • Graph your solution HW: P. 153 #1-31 odd Write DLUQ: How many problems do you need to solve in when you have a compound inequality?

  13. T2L Solve and Graph 1. 2.

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