Three-fourths of a number increased by 1 is 7. what is the number.

Remember the key words in mathematics:

Of = times (multiply)
Is = equals

(There are a lot more, but not that are pertinent to this problem.

three-fourths of a number increased by 1 is 7.
3/4 * x + 1 = 7

So: (3/4)x + 1 = 7

Solving it as a two step equation:

(3/4)x + 1 = 7
-1 -1
(3/4)x = 6
(4/3) * (3/4)x = (4/3) * 6
1x = 8
x = 8

I am assuming you can do the necessary arithmetic so I left out detailed descriptions of those steps. If you still don't get it, write back and I'll help you with that.

"three-fourths of a number increased by 1 is 7. what is the number."
(3/4 * x) + 1 = 7

or

3/4 * (x + 1) = 7

The question is ambiguous to me.

Because of:

a) the obvious level of the problem and
b) the wording of the problem

I would have to say that it is intended to be 3/4x + 1 = 7

The problem doesn't work out "cleanly" the other way and the wording (although slightly ambiguous, granted) leans far more towards my set-up. The other way 3/4(x + 1) = 7 would be worded three-quarters of the sum of a number and 1 or three-quarters of a number that is increased by 1.

Sorry, I just don't buy the ambiguity. You're reading too much into it.

Exactly - order of operations removes the ambiguity.

Solve limit equation: lim x is at 2
x^3-2x^2+4x-8/x^4-2x^2=x-2

Solve limit equation: lim x is at 2
x^3-2x^2+4x-8/x^4-2x^2=x-2

Please start your own thread for your question. You've tacked this onto a 2 year old post that is also unrelated to your question. It tends to cause people to waste time reading through a thread just to get to an entirely different question.