Solve for a to determine if the equation has one, none, or infinite solutions.
3(x + 2) - 6 = 3x (1 point)
The equation has one solution: x = 3
The equation has one solution: x = -3
The equation has no solution.
The equation has infinite solutions.
To solve for a, we need to simplify the equation:
3(x + 2) - 6 = 3x
Distribute 3 to both terms inside the parentheses:
3x + 6 - 6 = 3x
Combine like terms:
3x = 3x
Now, we see that the variable x is eliminated on both sides of the equation. This means that the equation is true for any value of x. Therefore, the equation has infinite solutions.
The correct answer is: The equation has infinite solutions.
To determine if the equation has one, none, or infinite solutions, we need to solve the equation and observe the result. Let's solve it step by step:
1. Distribute 3 to each term inside the parentheses:
3x + 6 - 6 = 3x
2. Simplify the equation:
3x = 3x
3. Notice that the variable term is the same on both sides of the equation. This indicates that the equation is an identity and will have infinite solutions. This means that any value of x will satisfy the equation.
Therefore, the correct answer is:
The equation has infinite solutions.
To solve this equation and determine the number of solutions it has, we need to simplify the equation and analyze the result.
3(x + 2) - 6 = 3x
Let's distribute the 3 on the left side of the equation:
3x + 6 - 6 = 3x
The +6 and -6 on the left side of the equation cancel each other out:
3x = 3x
Now let's get all the x terms on one side of the equation by subtracting 3x from both sides:
3x - 3x = 0
By subtracting like terms, we get:
0 = 0
Since 0 equals 0, this equation is always true, regardless of the value of x. This means that any value of x will satisfy the equation.
Therefore, the equation has infinite solutions.