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:

If Betty increases her time by 2 minutes 3 times a week, then she increases her time by a total of 6 minutes per week. We also know that she starts out running for 20 minutes. We can use this information to set up the equation in  form as:

Here x is the number of weeks, and y is the number of minutes she can run at the end of each week. The question is asking for how many minutes she can run at the end of 2 weeks, so we plug in 2 for x:

We can set up a system of equations to solve this problem. If we call the price of a single pair of socks "s" and a single belt "b" then we can set up the following equations:

The easiest way to solve this system would be to combine them in such a way that eliminates one of the variables. We can do this by multiplying the bottom equation by -2, then adding it to the top equation.

This simplifies to:

Now when we add it to the first equation, the s variables will cancel out:

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We can now solve for b, then plug that value into either one of the original equations.

Thus, we get that the cost of a belt, b, is 10 dollars and the cost of a pair of socks, s, is 5 dollars.

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:

The equation for Dave's distance after t hours can be written as:

Since Mike is biking for half an hour less than Dave, we can write his distance as:

We want to know how many hours it takes for Mike to catch up to Dave. In other words, we are looking for the time when they have traveled the same distance. So, we can set the equations for distance traveled equal to each other:

"t" is how long Dave bikes for until Mike catches up. "t-.5" is the amount of time that Mike bikes for, and that is what we are trying to find.

So, Mike bikes for 5/6 hours until he catches up with Dave.

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  on both sides of the equation.

Subtract four from both sides.

Divide by twelve on both sides.

Reduce.

Use order of operations to expand the terms of the parenthesis first.

Rewrite the equation.

Simplify the left side of the equation.

Add ten on both sides of the equation.

Simplify.

The answer is:  

In order to isolate the  variable, we will need to use order of operations to eliminate the parentheses and group the terms with an  variable to one side of the equation.

Distribute  inside the parentheses.

Subtract five on both sides.

Add  on both sides to move the negative  to the left side.

Take out a common factor of  on the left side.

Divide by  on both sides of the equation.

The answer is:  

To simplify:

1. Factor out  from  and we will get:

2. Reduce the equation and the final solution is: