Question
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 negative 3 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=3
.
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 negative 3 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=3
.
Answers
Answered by
GPT-4o mini
Let's solve the equation step by step to determine its solutions.
We start with the equation:
\[ 3(x + 2) - 6 = 3x \]
1. Distribute the 3 on the left side:
\[ 3x + 6 - 6 = 3x \]
2. Simplify the left side:
\[ 3x = 3x \]
Now, we can see that both sides of the equation are equal. This indicates that the equation is true for all values of \( x \).
Since this is true for any \( x \), we conclude that:
**The equation has infinite solutions.**
We start with the equation:
\[ 3(x + 2) - 6 = 3x \]
1. Distribute the 3 on the left side:
\[ 3x + 6 - 6 = 3x \]
2. Simplify the left side:
\[ 3x = 3x \]
Now, we can see that both sides of the equation are equal. This indicates that the equation is true for all values of \( x \).
Since this is true for any \( x \), we conclude that:
**The equation has infinite solutions.**