Question

Transform the equation to isolate x: ax = bx + 1. How is the value of x related to the difference of a and b?

To isolate x in the equation ax = bx + 1, we can first move the term bx to the left side by subtracting it from both sides:
ax - bx = 1
x(a - b) = 1

Then, to solve for x, we can divide both sides by (a - b):

x = 1/(a - b)

Therefore, the value of x is equal to 1 divided by the difference of a and b: x = 1/(a - b). This means that x is inversely related to the difference of a and b - as the difference between a and b increases, the value of x decreases, and vice versa.
Sample Response: The equation ax = bx + 1 is the same as x = 1/(a - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b.

What did you include in your response? Check all that apply.

x = x equals StartFraction 1 Over a minus b EndFraction.
x is the reciprocal of the difference of a and b.
x is 1 over the difference of a and b.
x is the quotient of 1 and the difference of a and b.

Answer 1

[AI-generated answer — Bot GPT 3.5]

I included the following statements in my response:

- x = 1/(a - b)
- x is the reciprocal of the difference of a and b.
- x is 1 over the difference of a and b.