Which of the following equation has no solutions?

Question

1. 6x+3=-6x+3
2. 6x+4=6x+4
3.-6x+4=6x+3
4.-6x+4=-6x+3

Answer 1

To determine which of the given equations has no solutions, we can solve each equation one by one.

1. Equation: \( 6x + 3 = -6x + 3 \)

   Rearranging gives: \[ 6x + 6x = 3 - 3 \] \[ 12x = 0 \] \[ x = 0 \] This equation has a solution: \( x = 0 \).

2. Equation: \( 6x + 4 = 6x + 4 \)

   This simplifies to: \[ 0 = 0 \] This equation is always true for any \( x \), so it has infinitely many solutions.

3. Equation: \( -6x + 4 = 6x + 3 \)

   Rearranging gives: \[ -6x - 6x = 3 - 4 \] \[ -12x = -1 \] \[ x = \frac{1}{12} \] This equation has a solution: \( x = \frac{1}{12} \).

4. Equation: \( -6x + 4 = -6x + 3 \)

   Rearranging gives: \[ 4 = 3 \] This is a false statement and has no solutions.

After checking all equations, we see that the answer is Option 4: \(-6x + 4 = -6x + 3\), which has no solutions.

Answer 2

Which of the following equations has exactly one solution?
1. -8x+3=-8x+3
2. 3x-8=3x-8
3.-3x+8=-3x-8
4. -3x +8=-3x-8

Answer 3

To find out which of the given equations has exactly one solution, let's analyze each equation one by one.

1. Equation: \(-8x + 3 = -8x + 3\)

   This simplifies to: \[ 0 = 0 \] This statement is always true for any \( x \). Therefore, it has infinitely many solutions, not just one.

2. Equation: \(3x - 8 = 3x - 8\)

   This simplifies to: \[ 0 = 0 \] Similar to the first equation, this statement is always true for any \( x \). Therefore, it also has infinitely many solutions.

3. Equation: \(-3x + 8 = -3x - 8\)

   Rearranging gives: \[ -3x + 3x = -8 - 8 \] \[ 0 = -16 \] This is a false statement, meaning there are no solutions.

4. Equation: \(-3x + 8 = -3x - 8\)

   Rearranging gives: \[ -3x + 3x = -8 - 8 \] \[ 0 = -16 \] This is also a false statement, meaning there are no solutions.

After evaluating all equations, we find that:

• Equations 1 and 2 have infinitely many solutions.
• Equations 3 and 4 have no solutions.

Conclusion: None of the equations provided has exactly one solution.

Answer 4

which one is closest to the answer

Answer 5

From the analysis of the equations you provided:

1. \(-8x + 3 = -8x + 3\) has infinitely many solutions (always true).
2. \(3x - 8 = 3x - 8\) also has infinitely many solutions (always true).
3. \(-3x + 8 = -3x - 8\) results in a false statement (no solution).
4. \(-3x + 8 = -3x - 8\) also results in a false statement (no solution).

Given the options you have provided:

• Equations 1 and 2 are equivalent and have infinitely many solutions.
• Equations 3 and 4 both have no solutions.

Indeed, none of the equations has exactly one solution. However, if you consider the definitions:

• Equations 3 and 4 are the closest candidates to having a defined solution condition (a definitive outcome), as they give false statements.

To summarize: If you’re looking for an option that is the closest to having a "solution state" (albeit not a unique one), it's Equations 3 and 4, as they halt the solution process outright by producing an impossible scenario. However, strictly speaking, none of the equations present exactly one solution.

Answer 6

pick one

Answer 7

If I must pick one that is closest to the answer for having a definitive condition regarding solutions, I would choose:

3. \(-3x + 8 = -3x - 8\)

This equation leads to a false statement, indicating that there are no solutions. While it doesn’t have exactly one solution, it does provide a clear conclusion about the nature of the solutions (none) compared to the others with infinitely many solutions.