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Solve for ss.\newline∣s∣+3≤4|s| + 3 \leq 4\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 ss.\newline∣s∣+3≤4|s| + 3 \leq 4\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 ∣s∣+3≤4|s| + 3 \leq 4. The first step is to isolate the absolute value term ∣s∣|s| by subtracting 33 from both sides of the inequality.\newline∣s∣+3−3≤4−3|s| + 3 - 3 \leq 4 - 3\newline∣s∣≤1|s| \leq 1
  2. Consider absolute value definition: Now that we have ∣s∣≤1|s| \leq 1, we need to consider the definition of absolute value. The absolute value of a number is the distance from zero on the number line, so ∣s∣≤1|s| \leq 1 means that ss is within 11 unit of zero. This gives us two inequalities: s≤1s \leq 1 and −s≤1-s \leq 1 (which is equivalent to s≥−1s \geq -1).
  3. Combine inequalities: Combining the two inequalities from the previous step, we get the compound inequality:\newline−1≤s≤1-1 \leq s \leq 1\newlineThis inequality represents all the values of ss that are within 11 unit of zero on the number line.

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