Question

Solve y = x + 6 fTwo boats are traveling in a canal in opposite directions, where x represents the distance, in feet, between the boats. The equation 2(x + 1) = 2x + 5 models the paths of the boats. Solve for x.or x.

Answer 1

The equation 2(x + 1) = 2x + 5 simplifies to a contradiction, 2 = 5, indicating there is no solution. This suggests there is likely a mistake in the model, as such an equation typically should not result in this type of outcome.

Step-by-step explanation:

The equation given is 2(x + 1) = 2x + 5, which models the paths of two boats traveling in a canal in opposite directions. To solve for x, we need to simplify and solve this linear equation.

1. First, distribute the 2 on the left side of the equation: 2x + 2 = 2x + 5.
2. Next, subtract 2x from both sides to get: 2 = 5.
3. This result is a contradiction, which implies the equation has no solution. There might be a mistake or a misconception in the model, as such an equation should not yield this kind of result in practical scenarios.

The process shows the importance of checking the validity of an equation before trying to solve it. Since x is supposed to represent the distance between boats, we might expect a positive numerical solution under normal circumstances. If the model is incorrect or based on a faulty premise, the equation may not represent a real-world situation accurately.