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Solve for qq. \newline−6∣q∣≤−12-6|q| \leq -12\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. \newline−6∣q∣≤−12-6|q| \leq -12\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. Perform Division: Now we perform the division to find the value that ∣q∣|q| is greater than or equal to.∣q∣≥2|q| \geq 2
  2. Absolute Value Analysis: The absolute value of qq being greater than or equal to 22 means that qq can be either greater than or equal to 22 or less than or equal to −2-2. This is because the absolute value of a number is its distance from zero on the number line, regardless of direction.\newlineSo, we have two inequalities:\newlineq≥2q \geq 2 or q≤−2q \leq -2
  3. Write Compound Inequality: We can now write the compound inequality that represents the solution to the original inequality.\newlineThe compound inequality is:\newlineq≤−2q \leq -2 or q≥2q \geq 2

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