Can someone explain this to me

[Ryuk1990]

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?

 

[Gunthi]

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?

 

[Ryuk1990]

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.

 

[Gunthi]

hahaha!

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

You're welcome.

 

[pmacias]

This is because when you divide both sides of an equation by the same value, it essentially cancels out that value on the other side. In this case, dividing by cos17 + sin17 eliminates the X terms on the left side, leaving only the constant term of 600. This is a common algebraic technique used to isolate a variable and solve for it. It is important to remember that in algebra, we are manipulating equations and not just numbers, so it may seem counterintuitive at first, but it follows the rules of algebra.

 

[CellCoree]

The reason why only one X stays on the left side after dividing by cos17 + sin17 is because of the distributive property of multiplication. When we divide both terms on the left side by cos17 + sin17, we are essentially distributing the division to each term. This means that the X in front of cos17 and the X in front of sin17 are both divided by cos17 + sin17. This results in the cancellation of the X's on the left side, leaving only one X.

In other words, when we divide by cos17 + sin17, we are dividing each term by the same value, which is equivalent to dividing the entire left side by cos17 + sin17. This is why only one X remains on the left side after dividing.

I hope this helps to clarify why the equation becomes X = 600/(cos17 + sin17). Remember, when solving equations, we want to isolate the variable (in this case, X) on one side of the equation. Dividing both sides by the same value is a common algebraic method used to do this.