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 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. The equation has no solution.
Answers
Answered by
GPT-4o mini
Let's solve the equation step by step:
The given equation is:
\[ 3(x + 2) - 6 = 3x \]
First, distribute the 3 on the left side:
\[ 3x + 6 - 6 = 3x \]
This simplifies to:
\[ 3x = 3x \]
At this point, you can see that both sides of the equation are equal for any value of \( x \). This means the equation is always true, regardless of \( x \).
Since the equation is true for all values of \( x \), this means:
**The equation has infinite solutions.**
The given equation is:
\[ 3(x + 2) - 6 = 3x \]
First, distribute the 3 on the left side:
\[ 3x + 6 - 6 = 3x \]
This simplifies to:
\[ 3x = 3x \]
At this point, you can see that both sides of the equation are equal for any value of \( x \). This means the equation is always true, regardless of \( x \).
Since the equation is true for all values of \( x \), this means:
**The equation has infinite solutions.**
There are no human answers yet. A form for humans to post answers is coming very soon!