Which of the following equations has EXACTLY one solution?
A
3x + 5 = 2x – 6
B
4x – 8 = 4x – 16
C
8x + 10 = 8x + 10
D
4x – 4 + 2x = 6x – 4
The equation that has exactly one solution is:
D
4x - 4 + 2x = 6x - 4
In this equation, by combining like terms, we get:
6x - 4 - (4x - 4) = 2x
Simplifying further,
2x = 2x
The variable "x" cancels out on both sides, showing that it is an identity and not an equation. This means that the equation has infinitely many solutions.
show how you got the answer
Apologies for the confusion in my previous response. Let's go through each equation and determine which one has exactly one solution.
A) 3x + 5 = 2x – 6
To solve this equation, we want to isolate the variable "x" on one side. By moving the 2x term to the left side and the 5 term to the right side, we get:
3x - 2x = -6 - 5
x = -11
B) 4x – 8 = 4x – 16
This equation seems more complicated at first, but notice that the 4x term cancels out on both sides when we simplify:
-8 = -16
Since the equation simplifies to a false statement (-8 ≠ -16), there are no solutions to this equation.
C) 8x + 10 = 8x + 10
In this equation, we have the same term on both sides of the equation (8x + 10). No matter what value we assign to x, the equation will always be true. This means that this equation has infinitely many solutions.
D) 4x – 4 + 2x = 6x – 4
To solve this equation, we combine like terms on both sides:
6x - 4 = 6x - 4
This equation simplifies to:
0 = 0
Since this equation simplifies to a true statement (0 = 0), it means that any value of "x" will satisfy the equation. Therefore, this equation has infinitely many solutions.
After reconsidering the options, none of the given equations have exactly one solution.