how would i solve these problems???

Question

1. 3/4 < n + 5/6
2. 2(4y - 7) > 8y - 20
3. six times a number increased by 38 is no more than the number decreased by 14

Answer 1

1) 3/4 18/24 -20/24 -1/12
2) 8y-14>8y-20
14<20, indeterminate

3) 6n +38 <= n-14
5n <= 24
n <=24/5

Answer 2

1. Solve inequalities the same way you would solve 3/4=n+5/6. The only thing you need to watch out for, which you don't have in this question, is multiplying or dividing by a negative number to isolate your variable; then the < changes direction.

3/4 < n + 5/6

Subtract 5/6 from both sides to isolate n.

3/4 - 5/6 < n + 5/6 - 5/6

Now you will work with the fractions as you normally would and find a common denominator:

9/12 - 10/12 < n

-1/12 < n

2) Are you sure you copied the question correctly? It's not possible to solve. You have 8y on both sides. They will cancel each other out. You'd end up having this:

[2(4y-7)]/2 > (8y - 20)/2
4y - 7 > 4y - 10
-7 > -10

The answer is true, it's just a strange answer to have.

3) When answering these types of questions, ALWAYS go step by step and think it through:

six times--what does that mean? 6 *

6 * (six times) a number--what's the number? We don't know. It's an unknown, so let's call it n. So, 6 times n is what? 6n

six times a number [6n] increased--what does increased mean? +, right? because we're adding an amount to increase it?

six times a number [6n] increased [+] by 38 [that ought to be straightforward enough] is--*is* is a KEY word because it means equal. We now have so far:

6n + 38 =

But wait! The full thing is "no more than". What does that mean? It means it could be equal to, but it could also be less than, right? So that means <= (arranged properly, of course):

6n [six times a number] + 38 [increased by 38] <= [is no more than] the number [n] decreased--what's decreased? it means you're losing some, right? you'll have less? so which sign do you think it'll be? you're right: - !

6n + 38 <= n - 14

Let's go back over the equation to make sure it matches up with the words:

six times a number increased by 38 is no more than the number decreased by 14

Great! We've got the equation done correctly. Now you just need to solve as you normally would:

6n + 38 <= n - 14

Let's get the n's on the left and the constants on the right:

6n - n <= -14 - 38 (hopefully I haven't skipped too many steps for you)

5n <= -52
n<= -52/5 or -10 2/5

Now, the question actually isn't clear. What somebody else wrote about it being 6(n+38) could also be correct because there's nothing strongly indicating whether it's 6 times (a number increased by 38) or (6n) increased by 38.

Answer 3

You solve them just like you would solve an equation, EXCEPT that if you multiply or divide both sides by a negative number, you have to switch the inequality. "No more than" means less than or equal to.

#3:

6n + 38 <= n - 14

subtract 1n from both sides and subtract 38 from both sides:

5n <= -52

divide by 5

n <= -10 2/5 or -10.4

Note that on #2, when you distribute the 2, you get
8y - 14 > 8y - 20 which is always true no matter what y is.

Answer 4

Work these problems just as if they had an equal sign, but just keep the greater than and less than signs.

1. 3/4 < n + 5/6
3/4 - 5/6 < n
9/12 - 10/12 < n
- 1/12 < n

If you need the n on the left side, reverse the direction of the sign.
n > - 1/12

2. (Work using same method.)

3. 6 (x + 38) <= x - 14
Work using the same method.
I can't write the "less than or equal to" sign the way it goes, but you surely know to put the equal underneath the less than.

Answer 5

for #1 you need to subtract 5/6 from both sides answer -1/12
#2 distibute the 2 to get 8y-14>8y-20 then add 20 to both sides to get 8y+6>8y divide by 8y you gt 6>1 which is as true statement

#3 6x+38

Answer 6

1 and 2 - Change the inequality into an equal sign. Solve for the variable. Draw a number line and plug in numbers above and below the solution to the variable to see what the inequality solution is.

3 - Let "x" equal your unknown number. Make an equation on each side of the equal sign (=). Solve for x.

Answer 7

1.
3/4 - 5/6 < n
18/24 - 20/24 < n
-2/24 < n
-1/12 < n
1/12 > n

2.
8y - 14 > 8y - 20 (here the Y gets cancel, then it is either wrong or you copied it bad)

3.
6x+38 = x-14
5X = - 52
x = -260

Answer 8

How do you?
well... for them,... you have to do guess and check
I'm still in school
so i don't know how to do these stuff
sorry

Answer 9

You need to read your math book and do your homework yourself