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 no solution.
The equation has no solution.
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.
To solve the equation, we can start by distributing the 3 to both terms inside the parentheses:
3x + 6 - 6 = 3x
Simplifying, we get:
3x = 3x
Now, we can subtract 3x from both sides of the equation:
3x - 3x = 0
Simplifying further, we get:
0 = 0
Since this equation is always true, it means that any value of x will satisfy the equation. Therefore, the equation has infinite solutions.
To solve the equation 3(x+2)−6=3x, we can start by distributing the 3 on the left side of the equation:
3x + 6 - 6 = 3x
This simplifies to:
3x = 3x
Now, we can subtract 3x from both sides of the equation to eliminate the variable on one side:
3x - 3x = 0
This simplifies to:
0 = 0
Since the equation simplifies to 0=0, this means that the variable x is eliminated and the equation is true for all values of x. Therefore, the equation has infinite solutions.
To determine if the equation has one, none, or infinite solutions, we need to solve for x and see if we arrive at a unique solution.
Given equation: 3(x+2) - 6 = 3x
Step 1: Distribute 3 to the terms inside the parentheses:
3x + 6 - 6 = 3x
Step 2: Combine like terms:
3x = 3x
Step 3: Subtract 3x from both sides of the equation:
3x - 3x = 0
Step 4: Simplify:
0 = 0
The equation simplifies to 0 = 0, which is a true statement. This means that any value of x will satisfy the equation. Thus, the equation has infinite solutions.
Therefore, the correct response is: "The equation has infinite solutions."