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Home » \[ \frac4\pi24 = \frac\pi6 \] - Dyverse

\[ \frac4\pi24 = \frac\pi6 \] - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Thus, $ x^2 = \boxed{20} $.

📌 Question: Find the largest value of $ x $ that satisfies $ |2x - 5| + |x + 3| = 12 $.

📌 Solution: We analyze the expression by considering the critical points where expressions inside absolute values change sign: $ x = \frac{5}{2} $ and $ x = -3 $. We consider three intervals:

📌 $ x < -3 $:

📌 Then $ 2x - 5 < 0 $, $ x + 3 < 0 $, so:

📌 -(2x - 5) - (x + 3) = -2x + 5 - x - 3 = -3x + 2 = 12 \Rightarrow -3x = 10 \Rightarrow x = -\frac{10}{3} \approx -3.33

📌 But $ -\frac{10}{3} < -3 $, so valid.

📌 $ -3 \le x < \frac{5}{2} $:

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