Solve for w.∣w∣−4<3Write a compound inequality like 1<x<3 or like x<1 or x>3. Use integers, proper fractions, or improper fractions in simplest form.______
Q. Solve for w.∣w∣−4<3Write a compound inequality like 1<x<3 or like x<1 or x>3. Use integers, proper fractions, or improper fractions in simplest form.______
Addition to isolate absolute value: We have the inequality ∣w∣−4<3. Let's isolate the absolute value term ∣w∣ by adding 4 to both sides of the inequality.∣w∣−4+4<3+4∣w∣<7
Split into two inequalities: The inequality ∣w∣<7 means that w is less than 7 units away from 0 on the number line. This can be split into two separate inequalities: w<7 and −w<7.
Multiplication to reverse inequality: The inequality −w<7 can be multiplied by −1 to get w>−7. Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign.−w<7(−1)(−w)>(−1)(7)w>−7
Combining into compound inequality: Now we have two inequalities: w<7 and w>−7. These can be combined into a compound inequality.−7<w<7
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