-8x+3=-8x+3 What has one solution
-3x-8=3x-8
-3x+8=-3x-8
3x-8=3x+8
The equation -8x+3=-8x+3 has infinitely many solutions because both sides of the equation simplify to the same expression.
The equation -3x-8=3x-8 has one solution because subtracting 3x from both sides gives -8 = 6, which is false.
The equation -3x+8=-3x-8 has no solution because adding 3x to both sides gives 8 = -8, which is false.
The equation 3x-8=3x+8 has no solution because subtracting 3x from both sides gives -8 = 8, which is false.
To determine which of the given equations has one solution, let's simplify each equation and compare them.
1) -8x + 3 = -8x + 3
In this equation, we have the same term, -8x, on both sides of the equation. When we subtract -8x from both sides, it cancels out, resulting in:
3 = 3
In this case, the equation simplifies to a tautology (a statement that is always true), indicating that it has infinitely many solutions rather than just one solution.
2) -3x - 8 = 3x - 8
Here, we can combine the x terms on one side of the equation by adding 3x to both sides:
-3x - 3x - 8 = 3x - 3x - 8
-6x - 8 = -8
The next step is to isolate the x term by adding 8 to both sides:
-6x - 8 + 8 = -8 + 8
-6x = 0
Dividing both sides by -6 gives us:
x = 0
Therefore, the equation -3x - 8 = 3x - 8 has one solution, x = 0.
3) -3x + 8 = -3x - 8
Similar to the first equation, we have the same term, -3x, on both sides. When we subtract -3x from both sides, it cancels out:
8 = -8
Again, this equation simplifies to a tautology, indicating that it also has infinitely many solutions rather than just one solution.
4) 3x - 8 = 3x + 8
In this case, the equation has the same term, 3x, on both sides. When we subtract 3x from both sides, it cancels out:
-8 = 8
This equation simplifies to a contradiction, indicating that it has no solution.
So, out of the given equations, only the equation -3x - 8 = 3x - 8 has one solution, which is x = 0.
To determine which of these equations has one solution, we need to look for any properties or patterns that indicate a unique solution. One such property is that both sides of the equation have the same expression (in this case, -8x + 3) and the coefficients (numbers multiplying the variables) are equal.
Let's examine each equation individually:
1. -8x + 3 = -8x + 3:
In this equation, we notice that both sides are identical. Thus, the coefficients (-8) are equal, and there are no variables on one side and constants on the other side. This equation is an example of an identity, which means it is true for any value of x. Therefore, it has infinitely many solutions.
2. -3x - 8 = 3x - 8:
This equation has "x" terms on both sides, but the coefficients (-3 and 3) are different. By simplifying, we can see that the variables cancel each other out:
-3x - 8 = 3x - 8
-3x - 3x - 8 = 0
-6x - 8 = 0
-6x = 8
x = -8/6
Simplifying further, we get x = -4/3. Since the equation resulted in a single value for x, it has one unique solution.
3. -3x + 8 = -3x - 8:
In this equation, we again notice that the coefficients (-3) are the same on both sides. However, after simplifying, we see that the variables (-3x) also cancel each other:
-3x + 8 = -3x - 8
-3x + 3x + 8 = 0
8 = 0
This equation leads to a contradictory statement (0 does not equal 8). Therefore, it has no solutions.
4. 3x - 8 = 3x + 8:
Similar to the previous equation, the coefficients (3) are the same on both sides. Simplifying the equation gives:
3x - 8 = 3x + 8
3x - 3x - 8 = 0
-8 = 0
Again, this equation leads to a contradictory statement. Hence, it has no solutions.
In summary, the equation -3x - 8 = 3x - 8 has one unique solution, x = -4/3.