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Solve for qq.\newline|-2q| > 4\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.\newline______

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Q. Solve for qq.\newline2q>4|-2q| > 4\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. Inequality Analysis: We have the inequality:\newline|-2q| > 4\newlineFirst, we solve for 2q|-2q|.\newline|-2q| > 4\newlineThis means that 2q-2q is either greater than 44 or less than 4-4, because the absolute value of a number is the distance from zero, and it can be either positive or negative.
  2. Splitting Cases: Now we split the inequality into two cases, one for each possible sign of 2q-2q:\newlineCase 11: -2q > 4\newlineCase 22: -2q < -4
  3. Case 11 Solution: For Case 11, we divide both sides by 2-2 to solve for qq. Remember that dividing by a negative number reverses the inequality sign:\newline-2q > 4\newlineq < -2
  4. Case 22 Solution: For Case 22, we also divide both sides by 2-2, again reversing the inequality sign:\newline-2q < -4\newlineq > 2
  5. Combining Cases: Combining both cases, we get the compound inequality: q < -2 or q > 2 This is the solution to the inequality |-2q| > 4.

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