# Wacky explanation in a student solutions manual for manipulating an equation

• MHB
• chr1s
In summary, the author arrived at the answer to the problem by multiplying by 2r(r+8), and the "2" was just because they wanted integer coefficients.
chr1s
In the answer book to Stewart's College Algebra 4th Edition, question 47 in Review for Chapter 2, it takes me, in a distance/rate/time problem, from 4/(r+8) + 2.5/(r) = 1 (which I got), to this common denominator procedure: "Multiplying by 2r(r+8), we get..." WHERE DID THEY GET THE "2"? It continues on to a quadratic procedure, all of which follows logically, and the answer, r = [-3 + (sq rt of 329)]/4, which seems to be right when I plug it back in. Can't figure out that 2... Thanks for anybody's help.

First of all, the following property does indeed hold for all real numbers $x$, $y$ and $z$: if $x=y$, then $xz=yz$. (Note that it is not the case that the converse is true for all $x$, $y$ and $z$.) Therefore, the author of a proof or a solution has the right to multiply a true equation by any number he or she wants. This is not an error. The author's responsibility is to arrive at the solution. The reader has the right to ask, "Why is this true?", but the question "Why did the author do this?" is secondary.

Now, $2.5/r$ can be represented as $$\displaystyle \frac{5}{2r}$$. The author probably wanted to arrive at an equation with integer coefficients after multiplication.

chr1s said:
In the answer book to Stewart's College Algebra 4th Edition, question 47 in Review for Chapter 2, it takes me, in a distance/rate/time problem, from 4/(r+8) + 2.5/(r) = 1 (which I got), to this common denominator procedure: "Multiplying by 2r(r+8), we get..." WHERE DID THEY GET THE "2"? It continues on to a quadratic procedure, all of which follows logically, and the answer, r = [-3 + (sq rt of 329)]/4, which seems to be right when I plug it back in. Can't figure out that 2... Thanks for anybody's help.
The "2" is just because they want integer coefficients. If you just multiply both sides by r(r+ 8) you get 4r+ 2.5(r+ 8)= r(r+ 8). Multiplying by 2 gives 8r+ 5(r+ 8)= 2r(r+ 8).

Another way of looking at it is that $$2.5= \frac{5}{2}$$ so that original form can be written as $$4/(r+ 8)+ 5/2r+ 1$$. Now the "common denominator" is 2r(r+ 8).

Thanks everybody. Certainly makes sense now.

## 1. What is a "wacky explanation" in a student solutions manual?

A "wacky explanation" in a student solutions manual refers to an unconventional or unusual way of explaining how to manipulate an equation. It may use non-traditional methods or language that may be confusing to some students.

## 2. Why would a student solutions manual include a wacky explanation for manipulating an equation?

A student solutions manual may include a wacky explanation to help students think outside the box and approach problem-solving in a creative way. It can also make the material more engaging and interesting for students.

## 3. Is it okay to use a wacky explanation in a student solutions manual for manipulating an equation?

While unconventional methods can be helpful for some students, it is important to ensure that the explanation is accurate and does not confuse or mislead students. It is best to use a combination of traditional and creative explanations to cater to different learning styles.

## 4. How can a wacky explanation in a student solutions manual affect student learning?

A wacky explanation can either help or hinder student learning. It may be beneficial for some students who struggle with traditional methods, but it can also confuse or distract others. It is important for teachers to assess the effectiveness of the explanation and provide additional support if needed.

## 5. Are there any drawbacks to using a wacky explanation in a student solutions manual for manipulating an equation?

One potential drawback of using a wacky explanation is that it may not align with the curriculum or the standard methods taught in the classroom. This can cause confusion for students when they are required to use traditional methods on exams or in higher level courses. It is important to balance creativity with accuracy when using wacky explanations.

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