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Solve for zz. \newline−∣z∣>−8-|z| > -8\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−∣z∣>−8-|z| > -8\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 term: We have the inequality: \newline−∣z∣>−8-|z| > -8\newlineFirst, we need to isolate the absolute value term ∣z∣|z|. To do this, we can multiply both sides of the inequality by −1-1. Remember that multiplying both sides of an inequality by a negative number reverses the inequality sign.\newline−1⋅(−∣z∣)<−1⋅(−8)-1 \cdot (-|z|) < -1 \cdot (-8)
  2. Multiply by −1-1: After multiplying by −1-1, we get:\newline∣z∣<8|z| < 8\newlineThis means that the value of zz, regardless of its sign, must be less than 88.
  3. Express as compound inequality: Now we need to express this as a compound inequality. The absolute value inequality ∣z∣<8|z| < 8 means that zz can be less than 88 and greater than −8-8 at the same time.\newlineThe compound inequality is:\newline−8<z<8-8 < z < 8

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