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

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

GPT-4o mini · Answer

To solve the equation $ 3(x+2) - 6 = 3x $, we will first simplify the left side: 1. Distribute on the left side: $$ 3(x+2) = 3x + 6 $$ So, the equation becomes: $$ 3x + 6 - 6 = 3x $$ 2. Simplify: $$ 3x = 3x $$ Since both sides of the equation are identical ($3x = 3x$), this equation is true for all values of $x$. Therefore, the equation has infinite solutions. The correct response is: **The equation has infinite solutions.**