Is the equation no solution, one solution, or infinitely many Solve the equation 6(x+3) = 6x + 18
The equation 6(x+3) = 6x + 18 simplifies to 6x + 18 = 6x + 18. When we subtract 6x from both sides, we get 18 = 18. This equation is true regardless of the value of x. Therefore, there are infinitely many solutions.
To determine if the equation has no solution, one solution, or infinitely many solutions, we need to solve the equation and see how many solutions result.
Let's simplify the equation step-by-step:
Step 1: Distribute 6 to both terms inside the parentheses:
6x + 18 = 6x + 18
Step 2: We notice that both sides of the equation are identical. This means that every value of x would make the equation true.
Therefore, the equation 6(x+3) = 6x + 18 has infinitely many solutions.
To determine if the equation has no solution, one solution, or infinitely many solutions, we need to simplify and analyze the equation.
Let's start by simplifying the equation:
6(x + 3) = 6x + 18
Distribute the 6 on the left side:
6x + 18 = 6x + 18
Next, we want to isolate the variable x. To do this, we can subtract 6x from both sides:
6x - 6x + 18 = 6x - 6x + 18
18 = 18
Now, let's examine the equation. We can see that the variable x has been eliminated, and both sides of the equation are equal to 18. The equation becomes 18 = 18.
When we have a statement like this, where both sides are equal, it means that the equation is an identity, which implies that there are infinitely many solutions.
Therefore, the equation 6(x + 3) = 6x + 18 has infinitely many solutions.