Solve (25a+4b)/(7y+14) = 9b: Identifying the Application Domain

Question

$\frac{25a+4b}{7y+4\cdot3+2}=9b$

What is the field of application of the equation?

00:00 Find the domain of the function

00:03 According to mathematical laws, division by 0 is forbidden

00:06 Since there's a variable in the denominator, we must ensure it's not 0

00:09 To do this, we'll set the denominator to 0 and solve

00:13 Calculate the multiplication

00:30 Isolate the variable Y

00:45 This is the Y value where the denominator equals 0

00:49 Therefore, the domain requires Y to be different from the solution

00:53 This way we ensure we're not dividing by 0

00:57 And this is the solution to the question

To solve the problem, follow these steps:

Step 1: Understand that the equation $\frac{25a+4b}{7y + 4 \cdot 3 + 2}=9b$ is undefined when the denominator equals zero.
Step 2: Simplify the denominator: $7y + 4 \cdot 3 + 2$ .
Step 3: Calculate the constant part: $4 \cdot 3 = 12$ , so the expression becomes $7y + 12 + 2$ .
Step 4: Combine constants: $12 + 2 = 14$ . The denominator is $7y + 14$ .
Step 5: Set the denominator equal to zero to find values of $y$ that make the equation undefined: $7y + 14 = 0$ .
Step 6: Solve for $y$ :

Therefore, the equation is undefined when $y = -2$ . The field of application excludes $y = -2$ .

The choice that reflects this is $\boxed{y \neq -2}$ .

$y\operatorname{\ne}-2$