GoldenLeaf

First, ratios are in the form of:

n:n (where 'n' equals any number)

While proportions are:

n(1)/n(2) = n(1`)/n(2`) (where n(1) is able to be multiplied/divided by a number to reach n(1`) (and vice versa for n(2) and n(2`)))

Now, on to the problem!

First, to be proportional means that the numbers are the same, just in different forms. This means that 3/1 and 24/8 must be the name number to be a proportion.

A simple way of doing that is to take the fraction's numerator and divide it by its denominator, and do it for all the listed fractions.

3/1 = 3

24/8 = 3

If all of the fractions simplify to the same number, then they are proportional.

3 = 3

Thus, 3/1 is proportional to 24/8

First, get like terms on the same side.

START: 7x + 4 = 5x + 5

Do one term at a time: I will start with the variable.

(7x - 5x) + 4 = (5x - 5x) + 5

2x + 4 = 5

Then, do the integers.

2x + (4 - 4) = (5 - 4)

2x = 1

Then, isolate the 'x'.

2x/2 = 1/2

x = 1/2

And that is your answer.

This sequence can go two ways: Are you doing an arithmetic sequence or a geometric sequence?

I will do both just in case.

For a geometric sequence, the rate 'r' is -1/2: Thus, the sequence would be:

{6, -3, 1.5, -0.75}

And that would be the answer.

HOWEVER, it is also possible to have an arithmetic sequence. The rate 'r' for that would be -9: Thus, the sequence would be:

{6, -3, -12, -21}

And thus, that is your other answer.

For the inequality, -3y < 15 , the goal is to isolate 'y'. Thus, to separate the 'y' and have it on its own, both sides must be divided by -3.

HOWEVER

Dividing or multiplying by a negative number also flips the sign! Thus, I personally find it easier to do the negative first, so that I don't lose track of the sign and get an incorrect answer. This makes the equation:

3y > -15

Now, it is easier to focus on one thing rather than two.

3y/3 > -15/3

Which turns into:

y > -5

That is your answer.

@Anonymous

Ah, my bad; I was reading a 10^6570 instead of (1+0.035), so you are correct.

300/1 is simply 300 in an over-complicated fraction form. All numbers are secretly over 1, but don't tell anybody 

The anon below me is correct, so I'm just going to remove this large wall of incorrect work :p

A really small number.

Though, in all seriousness, first you take 2.8 and move its decimal to the left 13 spaces.

0.00000000000028 is the number from that process.

Then, simply take the root of that number.

0.000000529150262 is your final answer

The fourth root of sixteen.

First, combine like terms. This means adding 54 to both sides

15a(-54+54) = (9+54)

15a = 63

Then, to separate 'a', divide by 15 on both sides

15a/15 = 63/15

a = 4.2

Unless the underscore before the 9 means something I am unaware of, then 4.2 is equivalent to 'a'