Question 421394: solve the compound inequality
4>-2x+3 or 9<-3x+5
the second arrow has a line under it
choose the solution to the compound
a. (-oo, oo)
b. (-oo, -4/3]
c. (-1/2, oo)
d. (-oo,-4/3] u (-1/2,oo)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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