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?

00:12 Let's find the domain of the function.

00:16 Remember, dividing by zero is not okay in math.

00:20 Since our denominator has a variable, it can't be zero.

00:25 So, we need to make sure the main denominator is not zero.

00:30 Now, let's figure out what makes the variable X not equal to zero.

00:36 Once we solve that, we have our answer. And that's how we tackle this problem.

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:

$x\operatorname{\ne}-3$

$x\operatorname{\ne}-3$