## anonymous one year ago Solve the following inequality. write the solution set using interval notation.

1. anonymous

2. anonymous

thats the question and how the answer must be.

3. jim_thompson5910

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?

4. anonymous

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.

5. jim_thompson5910

because 8*5 = 40 is the LCD

6. jim_thompson5910

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

7. anonymous

ohhhhhhhhhhh ok. am i correct in the final steps?

8. jim_thompson5910

 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

9. anonymous

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?

10. jim_thompson5910

when you distributed, what did you get?

11. anonymous

30x+10-16x-64≤-160

12. jim_thompson5910

the -64 should be +64

13. anonymous

14x-54≤-160

14. jim_thompson5910

since -8 times -8 = 64

15. anonymous

+54**

16. anonymous

didnt change the sign

17. jim_thompson5910

after distributing you should get 30x+10-16x+64≤-160 which simplifies to 14x+74≤-160 after you combine like terms

18. anonymous

14x≤-214

19. anonymous

oh i messed up somewhere

20. anonymous

21. anonymous

14x≤234?

22. jim_thompson5910

close but no

23. jim_thompson5910

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

24. anonymous

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

25. anonymous

x=-16.4142857?

26. jim_thompson5910

leave it as a fraction and reduce as much as possible

27. anonymous

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

28. jim_thompson5910

234/14 can be reduced to ???

29. jim_thompson5910

hint: find the GCF of 234 and 14

30. anonymous

GCF=2?

31. jim_thompson5910

yes

32. anonymous

117/7

33. jim_thompson5910

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

34. jim_thompson5910

good

35. anonymous

so what would the solution set be?

36. jim_thompson5910

so -234/14 = -117/7

37. jim_thompson5910

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

38. anonymous

[-117,7]?

39. jim_thompson5910

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

40. jim_thompson5910

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|

41. jim_thompson5910

so the interval would start at -infinity, then stop at -117/7 giving us $\Large \left. (-\infty, -\frac{117}{7}\right]$

42. anonymous

(-inf, -117/7)

43. jim_thompson5910

|dw:1443394823713:dw|

44. jim_thompson5910

|dw:1443394850880:dw|

45. jim_thompson5910

|dw:1443394878344:dw|

46. anonymous

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

47. jim_thompson5910

|dw:1443394904462:dw|

48. jim_thompson5910

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

49. jim_thompson5910

and there is a closed circle at -117/7 on the number line to tell readers to include the endpoint |dw:1443394959903:dw|

50. anonymous

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

51. jim_thompson5910

you're welcome