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

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

What is the field of application of the equation?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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

Step-by-step written solution

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1

Understand the problem

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

What is the field of application of the equation?

2

Step-by-step solution

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

Step-by-step solution:

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

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

Thus, the domain is x5 x \neq -5 .

3

Final Answer

x5 x\operatorname{\ne}-5

Practice Quiz

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Solve for X:

\( x - 3 + 5 = 8 - 2 \)

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