Solve the following inequality. write the solution set using interval notation.

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Solve the following inequality. write the solution set using interval notation.

Mathematics
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thats the question and how the answer must be.
Multiply both sides by 40 to clear out the fractions \[\Large \frac{6x+2}{8}-\frac{2x-8}{5} \le -4\] \[\Large 40*\left(\frac{6x+2}{8}-\frac{2x-8}{5}\right) \le 40*(-4)\] \[\Large 40*\left(\frac{6x+2}{8}\right)+40*\left(-\frac{2x-8}{5}\right) \le 40*(-4)\] \[\Large 5*\left(6x+2\right)-8*\left(2x-8\right) \le -160\] Do you see how to finish up?

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why is it 40? and i would distribute the 5 out into the 6X+2 then the 8 into the 2x-8 and keep going until i can take the left side and either divide the right by it or the left by the right.
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?
` i would distribute the 5 out into the 6X+2 then the 8 into the 2x-8` correct `keep going until i can take the left side and either divide the right by it or the left by the right` these steps seem a bit vague to me
if the number on the left of the less than or equal to sign is less than 160 divide 160 by it. if it is more than 160 than divide that number by 160?
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
after distributing you should get `30x+10-16x+64≤-160` which simplifies to `14x+74≤-160` after you combine like terms
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|
the inequality \(\LARGE x \le -\frac{117}{7}\) means that we shade to the left of -117/7 on the number line |dw:1443394759997:dw|
so the interval would start at -infinity, then stop at -117/7 giving us \[\Large \left. (-\infty, -\frac{117}{7}\right]\]
(-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
and there is a closed circle at -117/7 on the number line to tell readers to include the endpoint |dw:1443394959903:dw|
ok so that should be my answer than. Thanks! i understand it all now. and i know to use the inf.
you're welcome

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