What is an Expression for b in Terms of a?

[LLS]

Did I do this one correctly?

Homework Statement

If a = f - 2 and b = 4f + 5, what is an expression for b in terms of a?

It's multiple choice:

4a
4a - 4
4a + 2
4a + 7
4a + 13

The Attempt at a Solution

a = f - 2 and b = 4f + 5

add 2 to each side ----> a = f and b = 4f + 7

my answer is 4a + 7

 

[Tedjn]

You can add 2 to both sides of one equation, but you cannot just add two to one side of two equations. For example, what would happen if a = f, and b = 3f? When f = 1, we have a = 1, b = 3. Add two to both sides. a = f + 2 and b = 3f + 2. Now, to get the same answer of a = 1, we plug in -1 for f. This time, b = -1 instead of 3.

In this problem, what is the only thing that connects the two equations, i.e. what is the only thing to appear in both equations? How could you use that fact?

 

[LLS]

I am having trouble posting a response-getting an error message. I can't quote the above post.

"F" is common to both sides. I'm not sure what to do if that is the correct path.

 

[Tedjn]

Yes, you're right. What is f equal to? How can you get rid of the f in the second equation?

 

[tiny-tim]

If a = f - 2 and b = 4f + 5, what is an expression for b in terms of a?

Hi LLS!

It's a sort of chain-rule:

To write b in terms of a, you must write b in terms of f, and write f in terms of a.
​

So what is f in terms of a?

 

[LLS]

I need to divide by f on both sides.

a = -2 and b = 9

Would that make f = 0? And then b = 5?

Oy I'm confused.

I'll be out for the night at a family dinner in a bit. Please don't be upset if I don't get back to to the problem until tomorrow. I do appreciate the help.

 

[Tedjn]

No problem. Whenever you do anything to one side of an equation, you need to do it to the other side. In your case, dividing by f, what you end up with is

$$\frac{a}{f} = -2\hspace{0.35in}\text{ and }\hspace{0.35in}\frac{b}{f} = 4 + \frac{5}{f}\hspace{0.35in}\text{ if } f \neq 0$$​

You cannot just divide one side of an equation by something. Always do it to both sides of the equal sign.

Read Tim's comment again. Why would finding f in terms of a help if you know b in terms of f?

 

[HallsofIvy]

? Why in the world would you "need to divide by f"?

You know that a = f - 2 . Okay, so solve for f "in terms of a": f= ?

Now just replace f by that in b= 4f + 5.

 

[LLS]

b = 4(f - 2) + 5

b = 4f - 8 + 5

b = 4f - 13

Thank you

 

[tiny-tim]

b = 4(f - 2) + 5

Nooo … b = 4f + 5, and you must write f in terms of a.

So f = … ?

 

[HallsofIvy]

b = 4(f - 2) + 5

b = 4f - 8 + 5

b = 4f - 13

Thank you

Since that is not any of the given answers, I'm going to hope that was a typo!