Multiply both sides by to get:

Distribute the :

Combine like terms:

Divide both sides by :

a. Begin by using the FOIL method to square (2x-2).

The resulting equation should be:

b. Distribute -5 to the expression inside the parentheses to get

c. Finish simplifying by combining like terms:

Find the common multiple between the numerator and denominator.

divide numerator and denominator by 3:

divide numerator and denominator by 7:

divide numerator and denominator by 4:

Cannot be divided any more- lowest terms.

Divide both sides by :

The mathematical expression given in the question is . Adding together like terms, , this can be simplified to . The expression can be factored as . For every positive integer , must be a multiple of 5. If , then , which is not an integer multiple of 2, 8, 10, or 15. Therefore, the correct answer is 5.

The number of hours that Anna practices per week can be found by:

If Anna practices for 4.5 hours per week, then the number of weeks it will take for her to reach 10,000 hours can by found by:

We can use the same process to find the number of hours that Maggie practices per week, and from there the number of weeks it will take her to reach 10,000 hours:

Rearrange the terms by grouping like terms together:

then simplify:

.

Finally, move the numerical terms to the other side of the equation so that all of the like terms are together:

, then simplify: .

Add 38 on both sides.

Divide by two on both sides.

The equation becomes:

Add two on both sides.

Divide by three on both sides.

The answer is:

To simplify the equation you need to divide the numerator (top) and denominator (bottom), so:

The numerator can be factored to:

The denominator can be factored to:

After reducing, we will get

To simplify the equation you need to divide the numerator (top) and denominator (bottom), so:

The numerator can be factored to:

The denominator can be factored to:

After reducing, we will get