Question

| 3 -2x | < | 4-x |​

Answer 1

`| 3 -2x | < | 4-x |`

1.

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

2.

`x\in\left((3)/(2),4\right\rangle\\-3+2x<4-x\\3x<7\\x<(7)/(3)\\x<(7)/(3) \wedge x\in\left((3)/(2),4\right\rangle\\\boxed{x\in\left((3)/(2),(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,(3)/(2)\right\rangle \wedge x\in\left((3)/(2),(7)/(3)\right\rangle\\\\\boxed{\boxed{x\in\left(-1,(7)/(3)\right\rangle}}`