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Solve for yy.\newline∣y∣−6≥−1|y| - 6 \geq -1

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Q. Solve for yy.\newline∣y∣−6≥−1|y| - 6 \geq -1
  1. Isolate absolute value: We have the inequality: \newline∣y∣−6≥−1|y| - 6 \geq -1 \newlineFirst, we need to isolate the absolute value term ∣y∣|y| on one side of the inequality.\newline∣y∣−6+6≥−1+6|y| - 6 + 6 \geq -1 + 6 \newline∣y∣≥5|y| \geq 5
  2. Interpret inequality: Now we interpret the absolute value inequality ∣y∣≥5|y| \geq 5. The absolute value of a number is greater than or equal to 55 if the number itself is greater than or equal to 55 or less than or equal to −5-5. This gives us two inequalities: y≥5y \geq 5 or y≤−5y \leq -5
  3. Write compound inequality: We can now write the compound inequality that represents the solution to the original inequality.\newlineThe compound inequality is:\newliney≤−5y \leq -5 or y≥5y \geq 5

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