Find the Domain 2+xz=(x+1)+z

Problem

2+x*z=(x+1)+z

Solution

1. Identify the goal, which is to find the domain of the variable x in the given equation.

2. Rearrange the equation to isolate terms containing z on one side to see if there are any restrictions on x

2+x*z=x+1+z

3. Subtract z and 2 from both sides.

x*z−z=x+1−2

4. Factor out z on the left side and simplify the right side.

z*(x−1)=x−1

5. Analyze the equation for constraints. The equation is satisfied if x=1 (resulting in 0=0 for any z or if z=1 (resulting in x−1=x−1 for any x.

6. Determine the domain of x Since the equation is a linear polynomial relationship between x and z with no denominators, square roots of negative numbers, or logarithms, x can take any real value.

Final Answer

Domain:(−∞,∞)

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