4x+3=2 need two answers

Question

4x+3>=2 need two answers

keenan · Answer

thats one

anonymous · Answer

in absolute value he wants the absolute value and the negative reciprocal for like graphing

sriram · Answer

do u mean absolute value??

keenan · Answer

yes

anonymous · Answer

like flip the problem and signs

keenan · Answer

do you have answers

sriram · Answer

wait i think i have made some mistake

sriram · Answer

i got the mistake

sriram · Answer

mod(4x+3)>=2
hence when 4x-3>0
the mod would be removed to give
4x+3>2
and X> -1/4
 but this is only when 4x+3>0
that is for x lying btwn (-3/4 , infinity)
we now take the intersection of the 2 results
we get the intersection as (-1/4, infinity)
thats one

sriram · Answer

the other one would be when when 4x+3<0
ie when x lies (-infinity , -3/4)
at that moment on removing the mod we get
-4x-3>=2
hence x = (-infinity, -5/4)
taking intersection
(-infinity,-5/4)

sriram · Answer

sorry forgot the equal to sign
hence
x= ( -infinity , -5/4] U [-1/4, infinity)

anonymous · Answer

$$|4x+3|\geq 2$$ solve 
$$4x+3\geq 2$$ and 
$$4x+3\leq -2$$ separately that is all

anonymous · Answer

think about what you are actually analyzing in an absolute value inequality, this will allow you to approach these problems more insightfully.