Find the Domain 9=1/5z+12

Problem

9=1/(5*z+12)

Solution

1. Identify the type of function or equation. The expression contains a rational term where the variable z is in the denominator.

2. Determine the restriction for the domain. In a rational expression, the denominator cannot be equal to zero because division by zero is undefined.

3. Set the denominator equal to zero to find the excluded value:

5*z+12=0

4. Solve for z by subtracting 12 from both sides:

5*z=−12

5. Divide by 5 to isolate z

z=−12/5

6. State the domain. The domain consists of all real numbers except for the value that makes the denominator zero.

Final Answer

Domain: *{[z∈ℝ,z≠−12/5]}

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