hich of the following equations has exactly one solution?(1 point) Responses −3x+8=−3x−8 negative 3 x plus 8 equals negative 3 x minus 8 3x−8=3x+8 3 x minus 8 equals 3 x plus 8 −8x+3=−8x+3 negative 8 x plus 3 equals negative 8 x plus 3 −3x−8=3x−8
The equation that has exactly one solution is −3x+8=−3x−8.
To determine which equation has exactly one solution, we can examine each equation's structure and coefficients.
1. -3x+8 = -3x-8:
This equation has -3x on both sides and 8 on one side and -8 on the other. By simplifying the equation, we get:
-3x + 3x = -8 - 8
0 = -16
This equation is inconsistent and has no solution.
2. 3x-8 = 3x+8:
This equation has 3x on both sides and -8 on one side and 8 on the other. By simplifying the equation, we get:
3x - 3x = 8 + 8
0 = 16
This equation is inconsistent and has no solution.
3. -8x+3 = -8x+3:
This equation has -8x on both sides and 3 on one side and 3 on the other. By simplifying the equation, we get:
-8x + 8x = 3 - 3
0 = 0
This equation is true for all values of x and has infinitely many solutions.
4. -3x-8 = 3x-8:
This equation has -3x on one side and 3x on the other. By simplifying the equation, we get:
-3x - 3x = 8 - 8
-6x = 0
Dividing both sides by -6, we get:
x = 0
This equation has one solution: x = 0.
Therefore, the equation that has exactly one solution is -3x-8 = 3x-8.
To determine which of the following equations has exactly one solution, we need to solve each equation and see how many solutions it has.
1. −3x+8 = −3x−8
To solve this equation, we can start by simplifying and combining like terms:
8 = -8
This equation is not true. It means that no matter what value we substitute for x, we will not find a solution. Therefore, this equation has no solution.
2. 3x−8 = 3x+8
Similarly, we simplify and combine like terms:
-8 = 8
This equation is also not true, so it has no solution.
3. −8x+3 = −8x+3
Again, simplifying and combining like terms:
3 = 3
This equation is true for all values of x. So, it has infinitely many solutions.
4. −3x−8 = 3x−8
Simplifying and combining like terms:
-3x = 3x
This equation tells us that -3x and 3x are equal. The only way for these to be equal is if x itself equals to zero. So, there is exactly one solution for this equation.
Therefore, the equation "−3x−8=3x−8" has exactly one solution.