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6.4: Absolute Values and Inequalities

6.4: Absolute Values and Inequalities. Conjunction: |a x + b| < c Means: x is between + c -c < a x +b < c. Disjunction: |a x +b| > c Means: not between! a x + b < -c or a x + b > c. Solving absolute inequalities and graphing:.

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6.4: Absolute Values and Inequalities

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  1. 6.4: Absolute Values and Inequalities

  2. Conjunction: |ax + b| < c Means:x is between + c -c < ax +b < c

  3. Disjunction: |ax +b| > c Means: not between! ax + b < -c or ax + b > c

  4. Solving absolute inequalities and graphing: |x - 4| < 3 (less than is betweeness) Means: -3 < x- 4 < 3 (solve) Graph: +4 +4 +4 1< x< 7 0 1 2 3 4 5 6 7 8 9

  5. Solve and graph: |x + 9 |> 13 (disjunction) Means:x + 9 < -13 or x + 9 > 13 -9 -9 -9 -9 x < -22 x > 4 Graph: -25 -20 -15 -10 -5 0 5 10

  6. Change the graph to an absolute value inequality: 1. Write the inequality. (x is between) 2 <x< 8 Find half way between 2 and 8 It’s 5 (this is the median) To find the median, add the two numbers and then divide by 2. 2+8 = 5 0 1 2 3 4 5 6 7 8 9 10 2

  7. 3. Now rewrite the inequality and subtract 5 (the median) from each section. 2 - 5 <x - 5 < 8 - 5 Combine like terms or numbers and you get -3 <x - 5 < 3 4. Write your absolute inequality |x - 5| < 3 Notice: The median is 3 units away from either number.

  8. Write the inequality for this disjunction: -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 x< -6 or x> 4 (find the median) 2. x + 1 < - 5 x+1 > 5 3. |x+1|>5 +1 +1 +1 +1 (subtract -1 from both sides, so add 1) (write x + 1 inside the absolute brackets and 5 outside positive)

  9. Quick rule: |x - median|( inequality symbol here)range 2 Median: add the two numbers together and divide by 2. Remember to subtract. Watch signs! Range: subtract the two numbers, then divide by 2.

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