Solve and Apply: Finding the Field of Application for (x+y:3)/(2x+6)=4

Question

$\frac{x+y:3}{2x+6}=4$

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

00:11 There is a variable in the function's main denominator

00:14 Therefore in this case we must ensure the denominator is not equal to 0

00:20 Let's isolate the variable X

00:47 And this is the solution to the question

To solve this problem, we'll follow these steps to find the domain:

Step 1: Recognize that the expression $\frac{x+y:3}{2x+6}=4$ involves a fraction. The denominator $2x + 6$ must not be zero, as division by zero is undefined.
Step 2: Set the denominator equal to zero and solve for $x$ to find the values that must be excluded: $2x + 6 = 0$ .
Step 3: Solve $2x + 6 = 0$ :

Step 4: Conclude that the domain of the function excludes $x = -3$ , meaning $x \neq -3$ .

Thus, the domain of the given expression is all real numbers except $x = -3$ . This translates to:

$x\operatorname{\ne}-3$

$x\operatorname{\ne}-3$