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Solve for zz. \newline−2∣z∣<−6-2|z| < -6\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 zz. \newline−2∣z∣<−6-2|z| < -6\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 are given the inequality −2∣z∣<−6-2|z| < -6. The first step is to isolate the absolute value expression by dividing both sides of the inequality by −2-2. Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the direction of the inequality sign.\newline−2∣z∣<−6-2|z| < -6 \newline∣z∣>3|z| > 3
  2. Consider absolute value definition: Now that we have ∣z∣>3|z| > 3, we need to consider the definition of absolute value. The absolute value of a number is the distance of that number from zero on the number line, regardless of direction. Therefore, ∣z∣>3|z| > 3 means that zz is more than 33 units away from zero. This leads to two cases: z>3z > 3 or z<−3z < -3.
  3. Compound inequality solution: The compound inequality that represents the solution to ∣z∣>3|z| > 3 is z>3z > 3 or z<−3z < -3. This is because zz can be either greater than 33 or less than −3-3 to satisfy the original inequality.

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