Question

| 3 -2x | < | 4-x |​

Answer 1

$| 3 -2x | < | 4-x |$

1.

$x\in\left(-\infty,\dfrac{3}{2}\right\rangle\\-3+2x<4-x\\x>-1\\x>-1\wedge x\in\left(-\infty,\dfrac{3}{2}\right\rangle\\\boxed{x\in\left(-1,\dfrac{3}{2}\right\rangle}$

2.

$x\in\left(\dfrac{3}{2},4\right\rangle\\-3+2x<4-x\\3x<7\\x<\dfrac{7}{3}\\x<\dfrac{7}{3} \wedge x\in\left(\dfrac{3}{2},4\right\rangle\\\boxed{x\in\left(\dfrac{3}{2},\dfrac{7}{3}\right\rangle}$

3.

$x\in(4,\infty)\\-3+2x<-4+x\\x<-1\\x<-1 \wedge x\in(4,\infty)\\\boxed{x\in\emptyset}$

$x\in\left(-1,\dfrac{3}{2}\right\rangle \wedge x\in\left(\dfrac{3}{2},\dfrac{7}{3}\right\rangle\\\\\boxed{\boxed{x\in\left(-1,\dfrac{7}{3}\right\rangle}}$