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# use the multiplication property of inequalities to solve the inequality. Graph the solution set. 7/4x equal to or greater than -5/8 the solution set is

this is done using multiplication property of inequalities.  It is done for a line graph.

for an algebra I class

7/4 x≤ -5/8 is the problem and the multiplication property says you can do one of two things

you can either multiply both sides by the same positive number and keep the same inequality sign or

you can multiply both sides by the same negative number and reverse the inequality sign.

we want x by itself on one side and right now it is multiplied to 7/4

to cancel you multiply both sides of the reciprical of the number you want to cancel.

the reciprical means flip the fraction so 4/7* on both sides cancels the 7/4

so 4/7* 7/4 x≤ 4/7*-5/8

4/7 is positive so we keep the same inequality sign

4/7*7/4=1

so 4/7*7/4 x=x

4/7*-5/8=4*-5/(7*8)=-20/56 which reduces to -5/14

so x≤-5/14

does what I said make sense? please comment

when I worked this problem, that is what I came up with. I guess what is confusing me is that it calls for a solution set. Isn't a solution set 2 numbers in ( )

11/29/2012

sort of, what you are refering to is called an interval it expresses the idea of everything between two numbers  in this case the two numbers are - infinity and -5/14 and -5/14 is included in the set

the - infinity comes from the fact that there is no lowest number so we put -oo as a place holder on the left side. we put the biggest number on the right side.

if a boundry is included in the set we use a [ or a] on that bound to indicate that is in the set or we see = or = next to that boundry so in this case the answer is

(-oo,-5/14]

does that make sense?

11/29/2012

yes that does make sense, thank you so much, you're a life saver.

11/29/2012

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