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Solve for ww.\newline|w| - 4 < 3\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 ww.\newline∣w∣−4<3|w| - 4 < 3\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. Addition to isolate absolute value: We have the inequality |w| - 4 < 3. Let's isolate the absolute value term ∣w∣|w| by adding 44 to both sides of the inequality.\newline|w| - 4 + 4 < 3 + 4\newline|w| < 7
  2. Split into two inequalities: The inequality |w| < 7 means that ww is less than 77 units away from 00 on the number line. This can be split into two separate inequalities: w < 7 and -w < 7.
  3. Multiplication to reverse inequality: The inequality -w < 7 can be multiplied by −1-1 to get w > -7. Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign.\newline-w < 7\newline(-1)(-w) > (-1)(7)\newlinew > -7
  4. Combining into compound inequality: Now we have two inequalities: w < 7 and w > -7. These can be combined into a compound inequality.\newline-7 < w < 7

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