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# To solve the absolute value inequality $$|2x-1| < 3$$, you start by removing the absolute value under the condition set by the inequality, which gives us two separate inequalities: 1. $$2x - 1 < 3 0 Points ▲ good image bad image ▼ ## Ask AI on The Internet Question: Which inequality represents all possible values of x for the following absolute value inequality? |2x-1|<3 A.-1<x<2 B.-2<x<1 C.x<2 D.x<-1 Asked by thevttv56 0 Points Log In or Register to Vote To solve the inequality \(|2x - 1| < 3$$, we need to consider the two cases that arise from the definition of absolute value. The absolute value inequality $$|A| < B$$ can be rewritten as: $-B < A < B$ Here, $$A = 2x - 1$$ and $$B = 3$$. Applying this to our inequality gives: $-3 < 2x - 1 < 3$ Next, we solve for $$x$$ by isolating $$x$$ in the middle part of the inequality. 1. Add 1 to all parts of the inequality: $-3 + 1 < 2x - 1 + 1 < 3 + 1$ $-2 < 2x < 4$ 2. Divide all parts by 2 to solve for $$x$$: $\frac{-2}{2} < \frac{2x}{2} < \frac{4}{2}$ $-1 < x < 2$ Therefore, the inequality $$|2x - 1| < 3$$ represents all values of $$x$$ that satisfy: $-1 < x < 2$ Thus, the correct answer is: A. $$-1 < x < 2$$

May 22, 2024, 5:39 a.m.

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