Which statement about this equation is true?
3+x=2–3x
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution.
The equation has one solution.
The equation has infinitely many solutions.
The statement "The equation has one solution" is true.
The correct response is: The equation has one solution.
To determine which statement about the equation 3+x=2–3x is true, we need to solve the equation and see how many solutions it has.
To begin solving the equation, let's simplify both sides. Adding 3x to both sides, we get:
3+x+3x = 2–3x+3x
Combining like terms, we have:
4x + x = 2
Simplifying further:
5x = 2
Now, to solve for x, we divide both sides of the equation by 5:
(5x)/5 = 2/5
x = 2/5
Therefore, we have found that the value of x in this equation is 2/5. Since we have a specific value for x, we can conclude that the equation has one solution.
Hence, the statement "The equation has one solution" is true.