Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−7x=3x+6 (1 point)ResponsesThe equation has one solution: x=6.The equation has one solution: x equals 6 .The equation has no solution.The equation has no solution.The equation has one solution: x=10.The equation has one solution: x equals 10 .The equation has infinite solutions.The equation has infinite solutions.
To solve for x, first distribute the 5 on the left side of the equation:
10x + 10 - 7x = 3x + 6
Combine like terms on both sides:
3x + 10 = 3x + 6
Subtract 3x from both sides:
10 = 6
Since the equation leads to a contradiction (10 does not equal 6), there are no solutions to this equation. Therefore, the correct response is: The equation has no solution.