Which of the following equations has exactly one solution?(1 point)
Responses
−8x+3=−8x+3
negative 8 x plus 3 equals negative 8 x plus 3
−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8
3x−8=3x+8
3 x minus 8 equals 3 x plus 8
−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8
To determine which equation has exactly one solution, we need to look for equations where the variables can be simplified to a single value.
Let's analyze each equation:
1) −8x+3=−8x+3
In this equation, both sides are identical, so it is an identity. It means that the equation has infinitely many solutions.
2) −3x−8=3x−8
This equation has the same term on both sides (-8), so we can simplify it to:
-3x = 3x
By moving the variables to one side, we get:
-6x = 0
Dividing by -6, we find:
x = 0
Thus, this equation has one solution, x = 0.
3) 3x−8=3x+8
This equation has the same variable term on both sides (3x), but different constants (-8 and 8). When we simplify, we get:
-8 = 8
This statement is not true, so this equation has no solution.
4) −3x+8=−3x−8
This equation has the same variable term on both sides (-3x), but different constants (8 and -8). When we simplify it, we get:
8 = -8
Again, this statement is not true, so this equation has no solution.
Based on our analysis, the equation −3x−8=3x−8 has exactly one solution, x = 0.