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Solve for dd.\newline\lvert d \rvert - 9 < -2\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 dd.\newline∣d∣−9<−2\lvert d \rvert - 9 < -2\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|d| - 9 < -2\newlineFirst, we need to isolate the absolute value term on one side of the inequality.\newlineAdd 99 to both sides of the inequality to isolate ∣d∣|d|.\newline|d| - 9 + 9 < -2 + 9\newline|d| < 7
  2. Consider absolute value definition: Now we need to consider the definition of absolute value. The inequality |d| < 7 means that dd is less than 77 units away from 00 on the number line. This gives us two inequalities:\newlined < 7 and d > -7\newlineThese two inequalities can be combined into a compound inequality:\newline-7 < d < 7

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