Question

25. Solution of |2x - 3|<|x + 2| is​

Answer 1

$|2x - 3|<|x + 2| \\\\1.\ x\in(-\infty,-2\rangle\\-2x+3<-x-2\\x>5\\\\x>5\wedge x\in(-\infty,-2\rangle\\\underline{x\in\emptyset}\\\\2.\ x\in\left(-2,\dfrac{3}{2}\right\rangle\\-2x+3<x+2\\3x>1\\x>\dfrac{1}{3}\\\\x>\dfrac{1}{3}\wedge x\in\left(-2,\dfrac{3}{2}\right\rangle\\\underline{x\in \left(\dfrac{1}{3},\dfrac{3}{2}\right\rangle}\\\\\\3.\ x\in\left(\dfrac{3}{2},\infty\right)\\2x-3<x+2\\x<5\\\\x<5 \wedge x\in\left(\dfrac{3}{2},\infty\right)\\\underline{x\in\left(\dfrac{3}{2},5\right)}$

$x\in\emptyset \wedge x\in \left(\dfrac{1}{3},\dfrac{3}{2}\right\rangle} \wedge x\in\left(\dfrac{3}{2},5\right)\\\boxed{x\in\left(\dfrac{1}{3},5\right)}$