Solve for q.∣−2q∣>4Write 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 q.∣−2q∣>4Write a compound inequality like 1<x<3 or like x<1 or x>3. Use integers, proper fractions, or improper fractions in simplest form.______
Inequality Analysis: We have the inequality:∣−2q∣>4First, we solve for ∣−2q∣.∣−2q∣>4This means that −2q is either greater than 4 or less than −4, because the absolute value of a number is the distance from zero, and it can be either positive or negative.
Splitting Cases: Now we split the inequality into two cases, one for each possible sign of −2q:Case 1: −2q>4Case 2: −2q<−4
Case 1 Solution: For Case 1, we divide both sides by −2 to solve for q. Remember that dividing by a negative number reverses the inequality sign:−2q>4q<−2
Case 2 Solution: For Case 2, we also divide both sides by −2, again reversing the inequality sign:−2q<−4q>2
Combining Cases: Combining both cases, we get the compound inequality: q<−2 or q>2 This is the solution to the inequality ∣−2q∣>4.
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