Algebra

Manipulating Equations II

Given an arbitrary equation:

x = x

We could also multiply both sides by 2 to get:

2x = 2x

And 2x is the same thing as 2x, so this equation is valid. We could also multiply both sides by 3:

3x = 3x

Or 4:

4x = 4x

Or any number. We can prove this by multiplying both sides by c:

cx = cx

And cx is the same as cx, so this equation is valid. Therefore, it is valid to multiply both sides of an equation by an arbitrary number.

So that means, given an arbitrary equation:

x = x

I could multiply both sides by 1/c to get:

x/c = x/c

So, therefore, it is possible to divide both sides of an equation by an arbitrary number.

Question 7: (x + 6)/7 = x. Solve for x

Answer: Given the equation:

(x + 6)/7 = x

We could multiply both sides by 7 to get:

7(x + 6)/7 = 7x

(7/7)(x + 6) = 7x

x + 6 = 7x

And then we could subtract both sides of the equation by x to get:

x + 6 - x = 7x - x

x - x + 6 = 7x - x

0 + 6 = 6x

6 = 6x

6/6 = 6x/6

1 = x

x = 1

So the answer is 1.