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Solve for qq.\newline∣q∣+5>9|q| + 5 > 9\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.\newline______

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Q. Solve for qq.\newline∣q∣+5>9|q| + 5 > 9\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.\newline______
  1. Isolate absolute value: We have the inequality:\newline∣q∣+5>9|q| + 5 > 9\newlineFirst, we isolate the absolute value term by subtracting 55 from both sides of the inequality.\newline∣q∣+5−5>9−5|q| + 5 - 5 > 9 - 5\newline∣q∣>4|q| > 4
  2. Consider absolute value definition: Now we need to consider the definition of absolute value. The absolute value of qq is greater than 44 means that qq is either greater than 44 or less than −4-4. So we can write two inequalities: q>4q > 4 or q<−4q < -4 This is the compound inequality that represents the solution to the original inequality.

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