Solve for x to determine if the equation has one, none, or infinite solutions. 3(x+2)−6=3x (1 point) Responses The equation has one solution: x=3 . The equation has one solution: x equals 3 . The equation has no solution. The equation has no solution. The equation has one solution: x=−3 . The equation has one solution: x equals negative 3 . The equation has infinite solutions.

Question

GPT-4o mini · Answer

To solve the equation $ 3(x + 2) - 6 = 3x $, we start by simplifying both sides. 1. Distribute the $ 3 $ on the left side: $$ 3(x + 2) - 6 = 3x \implies 3x + 6 - 6 = 3x $$ 2. Simplify the left side: $$ 3x + 6 - 6 = 3x \implies 3x = 3x $$ The equation simplifies to $ 3x = 3x $, which is always true. This means that any value of $ x $ satisfies the equation, indicating that there are infinite solutions. Thus, the correct response is: **The equation has infinite solutions.**