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1.6 Absolute-Value Equations & Inequalities

1.6 Absolute-Value Equations & Inequalities. Absolute value of a number is its distance from zero on the number line. Absolute value of a number is never negative. If x ≥ 0, then |x| = x If x < 0, then |x| = -x. Properties of Absolute Value. For any real number a and b |ab| = |a| |b|

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1.6 Absolute-Value Equations & Inequalities

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  1. 1.6 Absolute-Value Equations & Inequalities

  2. Absolute value of a number is its distance from zero on the number line. Absolute value of a number is never negative. • If x ≥ 0, then |x| = x • If x < 0, then |x| = -x

  3. Properties of Absolute Value For any real number a and b |ab| = |a| |b| a |a| b |b| b ≠ 0 |-a| = |a| =

  4. Simplify 1) |4x|= 2) |-4x2|= 3) |x10|= 4) |x9|= 5) 6x3 = -3x2

  5. The distance between 2 numbers a and b is |a-b| or |b-a| 1) Find the distance between -8 and 1 Answer: 9 2) Find the distance between -6 and -35 Answer: 29

  6. Solving equations with Absolute Value If |x| = p (p is positive) then x = -p or x = p If |x| = 0 then x = 0 If |x| = -p then there is no solution If |x| = |p| then x = -p or x = p

  7. Examples • On the black board

  8. Solving inequalties with Absolute Value If |x| < p (p is positive) then -p < x < p If |x| > p then x < -p or x > p If |x| < -p then there is no solution

  9. Examples • On the black board

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