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

Question

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

GPT-4o mini · Answer

To solve the equation $3(x+2) - 6 = 3x$, we will simplify and solve for $x$. 1. Begin by distributing on the left side: $$ 3(x+2) = 3x + 6 $$ So the equation becomes: $$ 3x + 6 - 6 = 3x $$ Simplifying this gives: $$ 3x = 3x $$ 2. This simplifies to a true statement, indicating that the equation holds for all values of $x$. Since the equation simplifies to the form $3x = 3x$, which is always true, it means: The equation has infinite solutions. Thus, the correct response is: **The equation has infinite solutions.**