Question

Find the domain and solve for t, x, or y. ((x-m)/m) p=((x-n)/n) q

A) Domain: All real numbers; Solve for x
B) Domain: x ≠ m and x ≠ n solve for t
C) Domain:m ≠ 0 and n ≠ 0 Solve for x
D) Domain: x ≠ 0 Solve for y

Answer 1

The domain of the given equation is all real numbers except where m or n equals zero, to avoid division by zero. To solve for x, we manipulate the equation to isolate x. The correct answer is Option C, with the domain being m ≠ 0 and n ≠ 0, and solving for x.

Step-by-step explanation:

To find the domain and solve for x, we consider the equation given by the student, which appears to be: ((x-m)/m) * p = ((x-n)/n) * q.

Firstly, to find the domain of this equation, we note that we cannot divide by zero, so m and n cannot be zero. Therefore, the domain must exclude the values where m or n is equal to zero.

Furthermore, there are no restrictions on x itself as set by the equation, so x can be any real number.

Next, to solve for x, we want to isolate x on one side of the equation. We can do this by expanding both sides and then gathering terms with x on one side and the constants on the opposite side.

Finally, solving for x will provide us with the value in terms of m, n, p, and q.

The correct answer to the student's question is therefore, Option C: Domain: m ≠ 0 and n ≠ 0, Solve for x.