Guy's Responses in WyzAnt Answers

Hi Joana,

To solve this problem, remember that what you do on one side must be done on the other side. This ensures that you don't change the original equation given. (I will be happy to elaborate if that is unclear).

The goal is to isolate x. To do this, you want all of the terms with x's on one side:

7x + 10 = 5x - 3
-5x______-5x            Subtract 5x from both sides (5x-5x=0)
2x + 10 = -3

Next, you want all of the constants on the other side. This helps further isolate x:

2x + 10 = -3
     -10     -10       Subtract 10 from both sides (10-10=0)
2x = -13

Finally, you want to eliminate all of the coefficients on x. These numbers are being multiplied by x, not added. Therefore, you must divide them on both sides:

2x = -13
2       2       Divide 2 on both sides (2x/2 = x)
x=-13/2 or -6.5

Hope this helps! Please let me know if you have any further questions.

Hi Holly,

The distributive property states that when you multiply one factor by a polynomial, the factor must be multiplied by every term in the polynomial separately. In your example, you're multiplying -6 by the polynomial (a+8). The distributive property states that you must multiply -6 by each term (a and 8) separately.

-6(a+8) = (-6*a) + (-6*8) = (-6a) + (-48) = -6a - 48

Many people benefit from drawing arrows to indicate what gets multiplied. In this example, you would draw an arrow from the -6 to the a and another arrow from the -6 to the 8.

I hope this helps! Please let me know if you have any further questions.

Hi Prasenjeet,

I do not believe "elementary molecule" is still a common term in chemistry, but I did find the following wikipedia article that explains that Avogadro used to refer to atoms as "elementary molecules" and to compounds as "compound molecules" (http://en.wikipedia.org/wiki/History_of_molecular_theory#19th_century). If any other tutors know of a more recent distinction here, that would be appreciated.

Molecules are substances that are comprised of more than one atom. These atoms may be joined by ionic bonds or covalent bonds. Compounds, specifically, are molecules that combine more than one element; this excludes substances such as oxygen, hydrogen, and nitrogen, all of which naturally exist in a molecular form: O₂, H₂, and N₂.

I hope this helps. Please let me know if you have any other questions.

Hi Tyler,

To isolate x (i.e. to remove everything else on the right side of the equation), you need to add m/a. This is because x-m/a+m/a = x. But remember that what you do on one side of the equation must be done on the other side to keep the equation valid:

Z = x - m/a
+m/a    +m/a   Add m/a on both sides
Z+m/a = x

Hope that makes sense! Please let me know if you have any further questions.

Hy Kyndell,

Just to clarify, is this question asking to classify the number 3400? If so, here is how one goes about the problem:

The first categorization of a number is real or imaginary. Real numbers do not contain the number i (which represents the square root of -1). 3400 is a real number. Real numbers are numbers we would come across in real life, whereas imaginary numbers are solely intended to help solve higher-level mathematics problems.

The next categorization within real numbers is rational or irrational. Rational numbers are numbers that can be expressed as a fraction. Irrational numbers contain non-repeating, non-terminating decimals (examples include pi, e, and the square root of 3). 3400 is a rational number (as a fraction, it can be expressed as 3400/1).

Within rational numbers, a more specific category is integers. Integers are numbers that can be written without using fractions or decimals. Note that this includes negative numbers. 3400 is an integer.

Going one step further, whole numbers are integers excluding negative numbers. In other words, it is whole numbers beginning with 0 and moving up on the number line (0, 1, 2, 3, ...). 3400 is a whole number.

Finally, there is a final category within whole numbers called natural (or counting) numbers. This includes all whole numbers except 0 (i.e. 1, 2, 3, ...). 3400 is a natural number.

To summarize: 3400 is a real number, a rational number, an integer, a whole number, and a natural (or counting) number. Please let me know if any of this is unclear or if you have a question.