Can someone explain this to me

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Discussion Overview

The discussion revolves around solving the equation Xcos17 + Xsin17 = 600 for the variable X. Participants explore the reasoning behind why the left side simplifies to a single X after dividing by (cos17 + sin17), touching on concepts of distributivity in algebra.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents the equation Xcos17 + Xsin17 = 600 and questions why only one X remains after dividing by (cos17 + sin17).
  • Another participant suggests that the two X terms can be treated as one due to the distributive property.
  • A later reply expresses realization and gratitude for the clarification regarding the distributive property.

Areas of Agreement / Disagreement

Participants appear to agree on the application of the distributive property, with one participant expressing understanding after the explanation. However, the initial question about the simplification remains a point of inquiry.

Contextual Notes

The discussion does not delve into the mathematical steps or assumptions underlying the distributive property, nor does it clarify the implications of treating the two X terms as one.

Ryuk1990
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Say you have an equation like this.

Xcos17 + Xsin17 = 600

If I want to solve for X, I know that I can divide by cos17 + sin17.

So it ends up being X = 600/(cos17 + sin17).

However, why is it that it becomes just one X on the left side? There are two X's and dividing by cos17 + sin17 does not cancel the other X so why is it that only one X stays?
 
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Ryuk1990 said:
Say you have an equation like this.

Xcos17 + Xsin17 = 600

If I want to solve for X, I know that I can divide by cos17 + sin17.

So it ends up being X = 600/(cos17 + sin17).

However, why is it that it becomes just one X on the left side? There are two X's and dividing by cos17 + sin17 does not cancel the other X so why is it that only one X stays?

You can treat those two as only one, remember distributivity?
 
Gunthi said:
You can treat those two as only one, remember distributivity?

hahaha!

I can't believe I didn't even realize that. Thanks for the help.
 
Ryuk1990 said:
hahaha!

I can't believe I didn't even realize that. Thanks for the help.

You're welcome.
 

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