How many solutions can be found for the linear equation?
6(x+2)/2 = 12x/4 + 6
no solution
one solution
two solutions
infinitely many solutions
There is one solution for the linear equation.
To determine the number of solutions for the given linear equation, let's simplify the equation first:
6(x+2)/2 = 12x/4 + 6
By simplifying both sides of the equation, we get:
3(x+2) = 3x + 6
Expanding the equation further:
3x + 6 = 3x + 6
By subtracting 3x from both sides:
6 = 6
Since the equation simplifies to a true statement (6 = 6), we conclude that the equation has infinitely many solutions. Therefore, the correct answer is:
infinitely many solutions
To find out how many solutions a linear equation has, we need to solve the equation and see what the result is. Let's solve the given equation step by step.
6(x + 2)/2 = 12x/4 + 6
The first step is to simplify both sides of the equation.
3(x + 2) = 3x + 6
Next, distribute the 3 on the left side of the equation.
3x + 6 = 3x + 6
Now, we have the equation 3x + 6 = 3x + 6. The next step is to isolate the variable (x) on one side of the equation.
Subtracting 3x from both sides, we get:
6 = 6
At this point, we have 6 = 6. This means that both sides of the equation are equal, and there are infinitely many solutions.
Therefore, the answer is: infinitely many solutions.