Final Answer:
No solution because the final step,
2=7, leads to a contradiction, indicating that the linear equation has no valid solutions.Thus,the correct answer is 2
Step-by-step explanation:
In the given linear equation, Jose's final two steps are:
2 + 5x = 5x + 7
Subtracting 5x from both sides, we get:
2 = 7
This is a contradiction, and it implies that there is no valid solution for x that satisfies the given equation. When the variable cancels out, and we are left with a statement like 2 = 7, it means the equation has no solution. In mathematical terms, the system is inconsistent, indicating that there are no values of x that make both sides of the equation equal.
The contradiction arises from the fact that the variable x was eliminated during the solution process, leading to an equation that is always false. In other words, there is no number that can be substituted for \(x\) to make the equation true. Therefore, the answer to the question regarding the number of solutions is that there are no solutions (Option 2).
It's crucial to recognize these inconsistencies in solving linear equations as they indicate an error in the solution process or a contradiction within the original equation. In this case, the contradiction 2 = 7 alerts us to the fact that the equation is unsolvable, and there are no values of x that satisfy the given equation.