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Solve for zz.|z| + 3 > 5Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form.

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Q. Solve for zz.∣z∣+3>5|z| + 3 > 5Write 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.
  1. Isolate absolute value expression: First, we need to isolate the absolute value expression on one side of the inequality.\newlineStarting with the inequality |z| + 3 > 5 , we subtract 3 3 from both sides to isolate ∣z∣ |z| .\newline |z| + 3 - 3 > 5 - 3 \newline |z| > 2
  2. Consider absolute value definition: Next, we need to consider the definition of absolute value. The absolute value of zz being greater than 22 means that zz is either greater than 22 or less than −2-2.\newlineThis gives us two separate inequalities:\newlinez > 2 or z < -2
  3. Form compound inequality: Now we have the compound inequality that represents the solution to the original inequality.\newlineThe compound inequality is z > 2 or z < -2.

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