Question 421394
start with the first inequality.


4 > -2x + 3


add 2x to both sides of the equation and subtract 4 from both sides of the equation to get:


2x > 3 - 4


combine like terms to get:


2x > -1


divide both sides of the equation by 2 to get:


x > -1/2


go to the next inequality.


9 <= -3x + 5


add 3x to both sides of the equation and subtract 9 from both sides of the equation to get:


3x <= 5 - 9


simplify to get:


3x <= -4


divide both sides of the equation by 3 to get:


x <= -4/3


you have 2 possible solutions.


either x > -1/2 or x <= -4/3


in interval notation, x > -1/2 would be shown as (-1/2,oo).


in interval notation, x <= -4/3 would be shown as (-oo,-4/3]


putting them in ascending order gets you:


(-oo,-4/3] or (-1/2,oo)


the or can be replaced by union which is symbolized by the letter u.


your answer is therefore:


(-oo,-4/3] u (-1/2,oo)


this looks a lot like selection d.


given an interval of a,b, the following rules apply:


(a,b) means your value of x is greater than a and less than b.
(a,b] means your value of x is greater than a and less than or equal to b.
[a,b) means your value of x is greater than or equal to a and less than b.
[a,b] means your value of x is greater than or equal to a and less than or equal to b.


the interval notation of:


(-oo,-4/3] u (-1/2,oo) means that x is greater than negative infinity and less than or equal to -4/3 or x is greater than -1/2 and less than positive infinity.



i would go with selection d.