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Problems on Absolute Values

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Mika Seppälä: Problems on Absolute Values Equations 1 |2x – 8| = 2. Solve the following equations: |1 – |x|| = 3. 2 |1 – x| + 2|x 2 – 1| = 0. 3 |2 – x| + |x 2 – 4| = 4. 4

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Mika Seppälä: Problems on Absolute Values Inequalities 5 |3x – 7| 2. Solve the following inequalities: |1 – x| + |x+1| 3. 6 |2 –|x|| 1 7

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Mika Seppälä: Problems on Absolute Values Graphs 8 f(x) = |1 – |x – 1||, -1 x 3 Sketch the graphs of the following functions on the given intervals: g(x) = |1 – |x – 3| + |x – 1||, 0 x 4 9 h(x) = ||x 2 – 4| – 5|, -4 x 4 10

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Mika Seppälä: Problems on Absolute Values Challenge Problems 11 For which value of the parameter r the equation |x – 2| + |x – 4| = r has infinitely many solutions? Interpret the problem geometrically. Find these solutions. Show that x 2 + 1 2|x| for all x. 12

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