Solve the inequality. 1/3+x+2/9> 5/6

5⁄18 < x

Step-by-step explanation:

Start by adding like-terms [⅓ and 2⁄9] with 9 being the Least Common Denominator [LCD]. Since 2⁄9 already has a 9 in the denominator, it does not get touched, so in order to make ⅓ a denominator of 9, we simply multiply both terms by 3, to get 3⁄9. So, adding that to 2⁄9 gives you 5⁄9, also giving you 5⁄9 + x > ⅚. Now, we have to find the LCD again because we have two unlike fractions. Now, our Least Common Denominator is 18, so multiply both terms in ⅚ by 3 [15⁄18] and multiply both terms in 5⁄9 by 2 [10⁄18]. Now you have two like fractions to work with, and you can clearly see that your answer is x > 5⁄18. Although the answer is written in reverse, it is still the same concept.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: