Equations, Inequalities and VICs (3rd ed), Chapter 7

[Guest]

In Action Problem 26:

In this problem, we are solving for the park ranger's speed on the snowmobile (which is represented by the variable q).

The last step of the solution to this problem (on the bottom of p. 162), gives us the equation: q = - dr / d - rt. The right side of this equation is then converted to dr / rt - d.

So the last step of the solution to the problem looks like this:

q = - dr / d - rt = dr / rt - d

However, I don't understand how we can multiply one side of the equation (the right side) by - 1, but not the other side.

And if we did multiply the other side of the equation by - 1 as well, that would give us: - q = dr / rt - d. But we are looking for the value of q, not - q!

Could somebody explain to me what's going on here?

[adbce]

The concept here is not multiplying by -1 on both sides.

It will be clearer if you look at it from a different angle. A negative sign on one side of an equation can either belong to numerator or denominator but not both because then the signs would cancel each other.

x = - (1/2) is similar to saying x = 1 / (-2) which is similar to saying x = (-1) / 2.

Similarly, - (1 / [2-6]) is similar to saying 1 / (6-2) where denominator has used the negative sign and those two calculations result in 1/4.

Hope this helps....

[nvingers]

It does! Thank you very much!

[esledge]

Great explanation, adbce.

Another way to "see" it: We are multiplying one side of the equation by (-1)/(-1), which is identical to multiplying by +1.