**This page is designed to help provide support for Kate’s Elementary Algebra eCourse,** a video supplement that walk students through

*Elementary Algebra*in an engaging, visual/auditory way! View samples on MasterBooksAcademy.com.

## Corrections/Clarifications to Solutions

**Chapter 2, Lesson 5, Set III, Problem 15 **(optional problem) – In the chart in 15a, the x numbers should start at 0. Then in 15d, 49 should be plugged in instead of 50 into the equation (because the first week is when x = 0, the second would be when x = 1, etc.), yielding $324.50 instead of $325. 15b and 15c are correct as they are.

**Chapter 3, Lesson Lesson 1, Set I, Problem 3 **– This problem is using information from previous math courses.

On 3a, if she catches 3 a day, then the time it would take her to catch say 12 would be 12 divided by 3, or 12/3 (fractions are another way of showing division). We’re using x to stand for any amount she could need to catch, so we’d have x divided by 3, or *x*/3.

On 3b, if she does 3 a day and there are 7 days in a week, then she’d catch 3 * 7, or 21, each week. So in y weeks, she’d catch 21 times that number of weeks, or 21*y* (which means 21 times* y*).

On 3c, the question refers back to Lesson 4 of Chapter 2. If we use *y* for the mice caught and *x* for the number of days, we’d have *y* = 3*x*. So that would be a direct variation.

**Midterm Test, Problem 4
**Read the question very carefully. Note that it is asking for

*positive integers*. See page 91 for a definition of what those are.

**Chapter 16, Lesson 1, Problem 3** – You can also set up the equation like this: (6 mi/hr)(*x*) = (54 mi/hr)(40 min –* x*) Note that we’re setting these as equal because the distance up and down the mountain is the same, and we find distance by multiplying speed times time (*x* here is standing for the time up the mountain and 40 min – *x* for the time down).

You can then rewrite 6 mi/hr as 6 mi/60 min, since 60 min equals 1 hour, and 54 mi/hr as 54 mi/60 min. Then when you do the math, the units work out. You could at that point just rewrite without units (6/60)*x* = (54/60)(40 – *x*) to make it easier, but you’ve already checked to see that the units will work out. The *Solutions Manual* wrote 6(*x*/60) = 54((40 – *x*)/60, which means the same thing but makes it harder to see where the 60 came from.

**Chapter 16, Lesson 3, Problem 5f (page 639)** – (Note that this is not a problem I recommend solving in the eCourse schedule; however, here’s a clarification if you’ve attempted it.) The answer you should get when working out the problem there is *x* < 3 (rather than *x* > 3 as in the *Solutions Manual*), but note that we already were told to solve for when *x* < 0, so we really know just that *x* < 0.

## Questions and Answers

### I struggle with word problems; what do I do?

See the new “Notes for Students” section in the eCourse for some hints that may help.

### My graph doesn’t match the one in the *Solutions Manual*, and I can’t figure out why.

It may just be that the *Solutions Manual* graphed a different range of input values. See the newly updated Course File/Download for a whole section explaining how to grade graphs.

### I struggle figuring out when I can simplify fractions and when I can’t. What do I do?

See the new “Notes for Students” section in the eCourse for some hints that may help.

### What do I do if I struggle with problems including negative numbers?

See the new “Notes for Students” section in the eCourse for some hints that may help.

### When should I list both the positive and negative square root?

See the new “Notes for Students” section in the eCourse for some hints that may help.