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**Problems on Absolute Values**

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**Mika Seppälä: Problems on Absolute Values**

Equations Solve the following equations: 1 |2x – 8| = 2. 2 |1 – |x|| = 3. 3 |1 – x| + 2|x2 – 1| = 0. 4 |2 – x| + |x2 – 4| = 4. Mika Seppälä: Problems on Absolute Values

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**Mika Seppälä: Problems on Absolute Values**

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

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**Mika Seppälä: Problems on Absolute Values**

Graphs Sketch the graphs of the following functions on the given intervals: 8 f(x) = |1 – |x – 1||, -1 ≤ x ≤ 3 9 g(x) = |1 – |x – 3| + |x – 1|| , 0 ≤ x ≤ 4 10 h(x) = ||x2 – 4| – 5|, -4 ≤ x ≤ 4 Mika Seppälä: Problems on Absolute Values

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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. 12 Show that x2 + 1 ≥ 2|x| for all x. Mika Seppälä: Problems on Absolute Values

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