Solve 6/(x+5) = 1: Determining the Field of Application

Question

$\frac{6}{x+5}=1$

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 not allowed

00:07 Since there is a variable in the denominator, we must ensure it is not equal to 0

00:12 Let's isolate the variable X

00:30 And this is the solution to the problem

To solve this problem, we will determine the domain, or field of application, of the equation $\frac{6}{x+5} = 1$ .

Step-by-step solution:

Step 1: Identify the denominator. In the given equation, the denominator is $x+5$ .
Step 2: Determine when the denominator is zero. Solve for $x$ by setting $x+5 = 0$ .
Step 3: Solve the equation: $x+5 = 0$ gives $x = -5$ .
Step 4: Exclude this value from the domain. The domain is all real numbers except $x = -5$ .

Therefore, the field of application of the equation is all real numbers except where $x = -5$ .

Thus, the domain is $x \neq -5$ .

$x\operatorname{\ne}-5$