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Absolute Value Problems

Absolute Value Problems. Absolute value can be thought of as the distance a number is from zero The graphs below show what this looks like for each equation. | x | = 1 x = -1 or x = 1 The distance between x and 0 is equal to 1

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Absolute Value Problems

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  1. Absolute Value Problems • Absolute value can be thought of as the distance a number is from zero • The graphs below show what this looks like for each equation • |x| = 1 x = -1 or x = 1The distance between x and 0 is equal to 1 • |x + 2| = 1 x + 2 = -1 or x + 2 = 1 The distance between x + 2 and 0 is equal to 1 • |2x – 1| = 1 2x – 1 = -1 or 2x – 1 = 1 The distance between 2x – 1 and 0 is equal to 1

  2. Absolute Value Problems • Solve an equation that contains an absolute value by setting the expression inside the absolute value signs to the number on the right side of the equation or its opposite • It should be obvious that if |x| = 1 then x = -1 or x = 1 • A more advanced absolute value equation can be solved by changing it into two equivalent equations • |3x – 2| = 8 becomes 3x – 2 = -8 or 3x – 2 = 8 3x = -6 or 3x = 10 x = -2 or x = 10/3

  3. Absolute Value Problems • The absolute value expression must be isolated before the equation can be rewritten and solved • For example, to solve |2x – 1| + 3 = 8 • Subtract 3 from both sides to get |2x – 1| = 5 • Rewrite the absolute value equation as 2x – 1 = -5 or 2x – 1 = 5 • Solve the two individual equations to get x= -2 or x= 3 • Try these: |x + 4| + 5 = 6 |2x – 3| = 5 |3x + 5| = 2 |x + 4| = 1 2x – 3 = 5 or 2x – 3 = -5 3x + 5 = 2 or 3x + 5 = -2 x + 4 = 1 or x + 4 = -1 2x = 8 or 2x = -2 3x = -3 or 3x = -7 x = -3 or x = -5 x = 4 or x = -1 x = -1 or x = -7/3

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