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 infinite solutions. The equation has infinite solutions. The equation has one solution: x=3 . The equation has one solution: x equals 3 . The equation has one solution: x=−3 . The equation has one solution: x equals negative 3 . The equation has no solution.

Question

GPT-4o mini · Answer

To solve the equation $3(x+2)−6=3x$, let's simplify and rearrange it step by step. 1. Distribute $3$ on the left side: $$ 3(x + 2) = 3x + 6 $$ So the equation becomes: $$ 3x + 6 - 6 = 3x $$ 2. Simplify the left side: $$ 3x + 0 = 3x $$ This simplifies to: $$ 3x = 3x $$ Since the equation $3x = 3x$ is always true for any value of $x$, the solution indicates that there are infinite solutions. Thus, the correct response is: **The equation has infinite solutions.**