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thats the question and how the answer must be.

because 8*5 = 40 is the LCD

if you multiply both sides by the LCD, then you clear out the fractions

ohhhhhhhhhhh ok. am i correct in the final steps?

when you distributed, what did you get?

30x+10-16x-64≤-160

the -64 should be +64

14x-54≤-160

since -8 times -8 = 64

+54**

didnt change the sign

14x≤-214

oh i messed up somewhere

had to do the +64

14x≤234?

close but no

you lost a sign somewhere, it should be `14x≤-234`

ah i put it in my calculator and forgot the negative!

x=-16.4142857?

leave it as a fraction and reduce as much as possible

is it a fraction? i got a decimal when i divided

234/14 can be reduced to ???

hint: find the GCF of 234 and 14

GCF=2?

yes

117/7

divide each part of the fraction by 2
234/2 = 117
14/2 = 7
so 234/14 = 117/7

good

so what would the solution set be?

so -234/14 = -117/7

in the end, the solution would be \[\Large x \le -\frac{117}{7}\] what is this in interval notation?

[-117,7]?

draw a number line with -117/7 on it
|dw:1443394703025:dw|

(-inf, -117/7)

|dw:1443394823713:dw|

|dw:1443394850880:dw|

|dw:1443394878344:dw|

is it a ] because -117/7 is included?

|dw:1443394904462:dw|

`is it a ] because -117/7 is included?` correct

ok so that should be my answer than. Thanks! i understand it all now. and i know to use the inf.

you're welcome