Which of the following equations has exactly one solution?
-8x + 3 = -8x + 3
-3x -8 = 3x -8
-3x + 8 = -3x -8
3x - 8 = 3x + 8
The equation -8x + 3 = -8x + 3 has exactly one solution.
To determine which of the given equations has exactly one solution, we need to simplify each equation and compare the coefficients of the variables.
1) -8x + 3 = -8x + 3
This equation simplifies to 0 = 0. The coefficients of both x terms are the same, and the constant terms are also the same. Therefore, this equation has infinitely many solutions.
2) -3x - 8 = 3x - 8
Rearranging this equation, we get -3x - 3x = 8 - 8 ==> -6x = 0. Dividing both sides by -6 gives us x = 0. The coefficients of the x terms are equal, but the constant terms are also equal. Therefore, this equation has infinitely many solutions.
3) -3x + 8 = -3x - 8
Simplifying this equation, we have 8 = -8. The constant terms are not equal, and the coefficients of the x terms are the same. Therefore, there are no solutions to this equation.
4) 3x - 8 = 3x + 8
By rearranging this equation, we have 3x - 3x = 8 + 8 ==> 0 = 16. This simplifies to a false statement. The constant terms are not equal, and the coefficients of the x terms are the same. Thus, there are no solutions to this equation.
Out of the four given equations, only equation 3) -3x + 8 = -3x - 8 has exactly one solution.
To determine which equation has exactly one solution, we need to analyze each equation and check if the variables cancel out or if there are any constants on both sides.
1) -8x + 3 = -8x + 3:
Both sides of the equation are the same. This means that no matter what value x takes, the equation will always be true. In other words, this equation has infinitely many solutions.
2) -3x - 8 = 3x - 8:
If we subtract 3x from both sides, the equation becomes:
-8 = 6x - 8
By adding 8 to both sides, we get:
0 = 6x
Dividing both sides by 6 gives us:
0 = x
This shows that x is equal to 0. Therefore, this equation has exactly one solution.
3) -3x + 8 = -3x - 8:
Both sides of the equation have the term -3x. If we subtract -3x from both sides, it cancels out, and we're left with:
8 = -8
This is not possible since 8 is not equal to -8. Thus, this equation has no solution.
4) 3x - 8 = 3x + 8:
Both sides of the equation have the term 3x. If we subtract 3x from both sides, it cancels out, and we're left with:
-8 = 8
This is not possible since -8 is not equal to 8. Hence, this equation has no solutions.
So, out of the given equations, only equation 2) -3x - 8 = 3x - 8 has exactly one solution (x = 0).