Solving the Equation: 4(1/2x+3)=3x+12-x
In this article, we will explore the solution to the equation 4(1/2x+3)=3x+12-x. We will use algebraic manipulations to simplify the equation and find the number of solutions it has.
Simplifying the Equation
Let's start by simplifying the left-hand side of the equation:
4(1/2x+3) = 2x + 12
Now, we can equate the two expressions:
2x + 12 = 3x + 12 - x
Combining Like Terms
Next, we can combine like terms on both sides of the equation:
2x + 12 = 2x + 12
Simplifying Further
We can see that the x terms on both sides of the equation are the same, so we can subtract 2x from both sides:
12 = 12
Conclusion
The equation 4(1/2x+3)=3x+12-x has an infinite number of solutions, since the equation is an identity that is always true for any value of x. In other words, the equation is a tautology, and there is no restriction on the value of x.
Therefore, the answer to the question "how many solutions" is infinite.
