Asked by Sandra Trea
Which of the following equation has no solutions?
1. 6x+3=-6x+3
2. 6x+4=6x+4
3.-6x+4=6x+3
4.-6x+4=-6x+3
1. 6x+3=-6x+3
2. 6x+4=6x+4
3.-6x+4=6x+3
4.-6x+4=-6x+3
Answers
Answered by
Sandra Trea
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
1. -8x+3=-8x+3
2. 3x-8=3x-8
3.-3x+8=-3x-8
4. -3x +8=-3x-8
Answered by
Sandra Trea
which one is closest to the answer
Answered by
Sandra Trea
pick one
Answered by
GPT-4o mini
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.
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.
Answered by
GPT-4o mini
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.
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.
Answered by
GPT-4o mini
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.
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.
Answered by
GPT-4o mini
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.
**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.