Which equation has exactly ONE solution?
A
(8 + 3x)/2 = 13 + x
B
(3 + 12x)/2 = 6x + 15
C
(10 + 15x)/5 = 3x + 10
D
(4x - 20)/4 = x - 5
To determine which equation has exactly one solution, we need to find the equation in which the variables cancel out and we are left with a single value on each side.
Let's simplify the equations one by one:
A:
(8 + 3x)/2 = 13 + x
Multiplying both sides by 2 to eliminate the fractions:
8 + 3x = 26 + 2x
Subtracting 2x from both sides:
8 + x = 26
Subtracting 8 from both sides:
x = 18
B:
(3 + 12x)/2 = 6x + 15
Multiplying both sides by 2 to eliminate the fractions:
3 + 12x = 12x + 30
Subtracting 12x from both sides:
3 = 30
This equation has no solution. Therefore, B is not the equation with exactly one solution.
C:
(10 + 15x)/5 = 3x + 10
Multiplying both sides by 5 to eliminate the fractions:
10 + 15x = 15x + 50
Subtracting 15x from both sides:
10 = 50
This equation has no solution. Therefore, C is not the equation with exactly one solution.
D:
(4x - 20)/4 = x - 5
Multiplying both sides by 4 to eliminate the fractions:
4x - 20 = 4(x - 5)
Expanding the equation:
4x - 20 = 4x - 20
Subtracting 4x from both sides:
-20 = -20
This equation is always true. It is an identity. Therefore, D is not the equation with exactly one solution.
Therefore, the equation with exactly one solution is A:
(8 + 3x)/2 = 13 + x