Which equation has exactly ONE solution?
A. (3 + 10x)/2 = 4x + 2
B. x (15x - 5)/9 = 5x + 4
C. (2 + 6x)/2 = 3x + 1
D. (4x - 10)/2 = 2x - 5
To determine which equation has exactly one solution, we can start by simplifying each equation:
A. (3 + 10x)/2 = 4x + 2
Multiplying both sides by 2 gives: 3 + 10x = 8x + 4
Subtracting 8x from both sides gives: 3 + 2x = 4
Subtracting 3 from both sides gives: 2x = 1
Dividing both sides by 2 gives: x = 1/2
B. x (15x - 5)/9 = 5x + 4
Multiplying both sides by 9 gives: x(15x - 5) = 45x + 36
Expanding on the left side gives: 15x^2 - 5x = 45x + 36
Subtracting 45x from both sides gives: 15x^2 - 50x - 36 = 0
C. (2 + 6x)/2 = 3x + 1
Dividing both sides by 2 gives: 1 + 3x = 3x + 1
Since the variables cancel out, we are left with the statement 1 = 1. This is a true statement.
Since the equation simplifies to a true statement, this equation has infinitely many solutions.
D. (4x - 10)/2 = 2x - 5
Dividing both sides by 2 gives: 2x - 5 = 2x - 5
Subtracting 2x from both sides gives: -5 = -5
This is a true statement.
Since the equation simplifies to a true statement, this equation also has infinitely many solutions.
Therefore, the only equation with exactly one solution is A. (3 + 10x)/2 = 4x + 2