Which equation has exactly ONE solution?
A 3+10x/2= 4x + 2
B 15x−5/3= 5x + 4
C 2+6x/2= 3x + 1
D 4x−10/2= 2x − 5
To determine which equation has exactly ONE solution, we can simplify each equation and check if the result is true.
A) 3 + 10x/2 = 4x + 2
First, multiply both sides of the equation by 2 to get rid of the fraction:
6 + 10x = 8x + 4
Next, subtract 8x from both sides:
6 + 2x = 4
Finally, subtract 6 from both sides:
2x = -2
x = -1
The solution to this equation is x = -1.
B) 15x - 5/3 = 5x + 4
First, multiply both sides of the equation by 3 to get rid of the fraction:
45x - 5 = 15x + 12
Next, subtract 15x from both sides:
30x - 5 = 12
Finally, add 5 to both sides:
30x = 17
x = 17/30
The solution to this equation is x = 17/30.
C) 2 + 6x/2 = 3x + 1
First, simplify the left side of the equation:
2 + 3x = 3x + 1
Next, subtract 3x from both sides:
2 = 1
This equation does not have a solution since 2 does not equal 1.
D) 4x - 10/2 = 2x - 5
First, simplify the left side of the equation:
4x - 5 = 2x - 5
Next, subtract 2x from both sides:
2x - 5 = -5
Finally, add 5 to both sides:
2x = 0
x = 0
The solution to this equation is x = 0.
Therefore, the equation that has exactly ONE solution is A) 3 + 10x/2 = 4x + 2.