Select the equation that has infinitely many solutions.(1 point)
Responses
3x=2x+1
4x+1=4(x+1)
3−3x=−3(x−1)
3x+5=3x−5
3x=2x+1
Are u sure?
The equation that has infinitely many solutions is "3x=2x+1."
To determine which equation has infinitely many solutions, we need to compare the equations and look for any patterns or inconsistencies.
Let's analyze each equation one by one:
1) 3x = 2x + 1
We can start by simplifying the equation:
3x - 2x = 2x - 2x + 1
x = 1
In this case, we have a solution (x = 1), so it does not have infinitely many solutions.
2) 4x + 1 = 4(x + 1)
Again, let's simplify the equation:
4x + 1 = 4x + 4
By subtracting 4x from both sides, we get:
1 = 4
This equation is inconsistent since the left-hand side (1) does not equal the right-hand side (4). Therefore, it does not have any solutions, let alone infinitely many solutions.
3) 3 - 3x = -3(x - 1)
Let's simplify this equation as well:
3 - 3x = -3x + 3
By adding 3x to both sides, we get:
3 = 3
Every value of x will satisfy this equation since both sides are equal. Therefore, this equation has infinitely many solutions.
4) 3x + 5 = 3x - 5
When we simplify this equation, we get:
3x + 5 = 3x - 5
By subtracting 3x from both sides, we have:
5 = -5
This equation is also inconsistent because 5 does not equal -5. Therefore, it does not have any solutions.
So, out of the given equations, the equation that has infinitely many solutions is:
3 - 3x = -3(x - 1)