The given equation 2(x + 2) = 2(x + 1) - 1 simplifies to a contradiction, 4 = 1. This indicates no solution, as there is no value of x that satisfies the equation.
To solve the equation 2(x + 2) = 2(x + 1) - 1 for x, let's simplify both sides of the equation:
Expanding the expressions within the parentheses:
2x + 4 = 2x + 2 - 1
Combining like terms:
2x + 4 = 2x + 1
Subtracting 2x from both sides:
4 = 1
Upon simplification, we arrive at the statement 4 = 1, which is not a true statement. In algebra, this result indicates a contradiction. A contradiction arises when there is no value of x that satisfies the equation. In this case, the equation is inconsistent and has no solution.
Therefore, the solution to the given equation, 2(x + 2) = 2(x + 1) - 1, is "No solution." The contradiction in the simplified form demonstrates that there is no value of x that makes the equation true.
complete question should be :
Solve the equation 2(x + 2) = 2(x + 1) - 1 for x, showing each step of the solution process. If there is no solution, explain why.