Question

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

Answer 1

thats the question and how the answer must be.

Answer 2

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?

Answer 3

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.

Answer 4

because 8*5 = 40 is the LCD

Answer 5

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

Answer 6

ohhhhhhhhhhh ok. am i correct in the final steps?

Answer 7

` 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

Answer 8

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?

Answer 9

when you distributed, what did you get?

Answer 10

30x+10-16x-64≤-160

Answer 11

the -64 should be +64

Answer 12

14x-54≤-160

Answer 13

since -8 times -8 = 64

Answer 14

+54**

Answer 15

didnt change the sign

Answer 16

after distributing you should get `30x+10-16x+64≤-160`

which simplifies to `14x+74≤-160` after you combine like terms

Answer 17

14x≤-214

Answer 18

oh i messed up somewhere

Answer 19

had to do the +64

Answer 20

14x≤234?

Answer 21

close but no

Answer 22

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

Answer 23

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

Answer 24

x=-16.4142857?

Answer 25

leave it as a fraction and reduce as much as possible

Answer 26

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

Answer 27

234/14 can be reduced to ???

Answer 28

hint: find the GCF of 234 and 14

Answer 29

GCF=2?

Answer 30

yes

Answer 31

117/7

Answer 32

divide each part of the fraction by 2

234/2 = 117
14/2 = 7

so 234/14 = 117/7

Answer 33

good

Answer 34

so what would the solution set be?

Answer 35

so -234/14 = -117/7

Answer 36

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

Answer 37

[-117,7]?

Answer 38

draw a number line with -117/7 on it

Answer 39

the inequality \(\LARGE x \le -\frac{117}{7}\) means that we shade to the left of -117/7 on the number line