What is 1/4x +1/3x?

Since both of these terms are like terms, we know we can add them up. The next step to simplifying is finding a common denominator, which we can see is 4x3 which is 12. So combining 3/12x +4/12x we get 7/12x which is the simplest form.

What is 4+ (3-4)?

We must follow the order of operations PEMDAS. So beginning with parentheses, we know that if we look at a number line, when we move 4 spots to the left of 3 we end up at -1. Now we are left with 4+(-1) and because a (-)(+) = (-), we know that this will change to 4-3. 1 spot to the left of 4 on the number line leaves us at 3.

What is the value of x in the equation, (3(2x+x)^2)/2=27 if x>0.

We want to first write down the order of operations, PEMDAS (parentheses, exponents, multiplication and division, addition and subtraction). Starting with P, we want to solve inside the parentheses and since we can add like terms together, we know that (2x + x)= 3x. Now we move onto exponents which means we will square the value inside the parentheses which we just found to be 3x. (3x)^2 gives us 9x^2. Now we move onto multiplication and multiplying 3(9x^2) gives us 27x^2. Now we have (27x^2)/2=27 To get rid of the denominator, we want to multiply both sides by the reciprocal (1/2) which leaves us with 27x^2=54. Now we want to keep x by itself, so to get rid of the 27 we are going to perform the opposite operation and divide both sides by 27. that leaves us with x^2= 2. To get rid of the exponent, we need to square root both sides, leaving us with x=+/- 2^1/2 Since we want x>0, we know x=sqrt 2. And thats the end!