Question

How do you solve `abs(4x+2)<6`?

Answer 1

See below

Explanation:

Use definition of absolute value

`absx=x` if `x>=0` and `absx=-x` if x<0

In our case

first case: `abs(4x+2)=4x+2` if `4x+2>=0` but this last it's the same that: `4x>=-2` or `x>=-1/2`

If `x>=-1/2` then `abs(4x+2)=4x+2<6` or `4x<4` or `x<1`

Then `abs(4x+2)<6` if `x in [-1/2,1]`

Second case: `abs(4x+2)=-(4x+2)` if `4x+2<0`. But this it's the same that `x<-1/2`

If `x<-1/2` then `abs(4x+2)=-(4x+2)=-4x-2<6` or `-8<4x` or `-2< x`

then `abs(4x+2)<6` if `x in (-2, -1/2)`