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Solve for qq.\newline\lvert q - 4 \rvert > 5\newlineWrite a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form.

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Q. Solve for qq.\newline∣q−4∣>5\lvert q - 4 \rvert > 5\newlineWrite a compound inequality like 1<x<31 < x < 3 or like x<1x < 1 or x>3x > 3. Use integers, proper fractions, or improper fractions in simplest form.
  1. Solve Absolute Value Inequality: We have the inequality: \newline|q - 4| > 5\newlineFirst, we need to solve for ∣q−4∣|q - 4|.
  2. Split into Two Cases: The absolute value inequality |q - 4| > 5 means that the expression inside the absolute value, q−4q - 4, is either greater than 55 or less than −5-5.\newlineSo we split the inequality into two cases:\newlineCase 11: q - 4 > 5\newlineCase 22: q - 4 < -5
  3. Case 11: q > 9: For Case 11, we solve for qq:q - 4 > 5Add 44 to both sides:q > 5 + 4q > 9
  4. Case 22: q < -1: For Case 22, we solve for qq: \newlineq - 4 < -5\newlineAdd 44 to both sides:\newlineq < -5 + 4\newlineq < -1
  5. Combine Cases for Solution: Combining both cases, we get the compound inequality:\newlineq < -1 or q > 9\newlineThis is the solution to the inequality |q - 4| > 5.

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