Asked by Scary spider 🕷️
Which of the following equations has exactly one solution? (1 point) 3x - 8 = 3x + 8; 8x + 3 = - 8x + 3; - 3x + 8 = - 3x - 8; - 3x - 8 = 3x - 8
Answers
Answered by
Scary spider 🕷️
Which of the following equations has exactly one solution
3x - 8 = 3x + 8
-8x + 3 = - 8x + 3
-3x + 8 = - 3x - 8
- 3x - 8 = 3x - 8
3x - 8 = 3x + 8
-8x + 3 = - 8x + 3
-3x + 8 = - 3x - 8
- 3x - 8 = 3x - 8
Answered by
GPT-4o mini
To determine which of the given equations has exactly one solution, we can analyze each equation one at a time:
1. **Equation 1:** \( 3x - 8 = 3x + 8 \)
Subtract \( 3x \) from both sides:
\[
-8 = 8
\]
This is a contradiction, so there are **no solutions**.
2. **Equation 2:** \( 8x + 3 = -8x + 3 \)
Subtract 3 from both sides:
\[
8x = -8x
\]
Adding \( 8x \) to both sides:
\[
16x = 0 \implies x = 0
\]
This equation has **exactly one solution**: \( x = 0 \).
3. **Equation 3:** \( -3x + 8 = -3x - 8 \)
Add \( 3x \) to both sides:
\[
8 = -8
\]
This is again a contradiction, so there are **no solutions**.
4. **Equation 4:** \( -3x - 8 = 3x - 8 \)
Add \( 3x \) to both sides:
\[
-8 = 6x - 8
\]
Adding \( 8 \) to both sides:
\[
0 = 6x \implies x = 0
\]
This equation also has **exactly one solution**: \( x = 0 \).
In conclusion, both Equation 2 and Equation 4 have exactly one solution (\( x = 0 \)). If you must choose one answer, either would be correct, but typically you would select the first that meets the criteria, so:
**Answer: \( 8x + 3 = - 8x + 3 \)** has exactly one solution.
1. **Equation 1:** \( 3x - 8 = 3x + 8 \)
Subtract \( 3x \) from both sides:
\[
-8 = 8
\]
This is a contradiction, so there are **no solutions**.
2. **Equation 2:** \( 8x + 3 = -8x + 3 \)
Subtract 3 from both sides:
\[
8x = -8x
\]
Adding \( 8x \) to both sides:
\[
16x = 0 \implies x = 0
\]
This equation has **exactly one solution**: \( x = 0 \).
3. **Equation 3:** \( -3x + 8 = -3x - 8 \)
Add \( 3x \) to both sides:
\[
8 = -8
\]
This is again a contradiction, so there are **no solutions**.
4. **Equation 4:** \( -3x - 8 = 3x - 8 \)
Add \( 3x \) to both sides:
\[
-8 = 6x - 8
\]
Adding \( 8 \) to both sides:
\[
0 = 6x \implies x = 0
\]
This equation also has **exactly one solution**: \( x = 0 \).
In conclusion, both Equation 2 and Equation 4 have exactly one solution (\( x = 0 \)). If you must choose one answer, either would be correct, but typically you would select the first that meets the criteria, so:
**Answer: \( 8x + 3 = - 8x + 3 \)** has exactly one solution.
Answered by
GPT-4o mini
To determine which of the given equations has exactly one solution, let's analyze each one:
1. **Equation 1:** \( 3x - 8 = 3x + 8 \)
Subtract \( 3x \) from both sides:
\[
-8 = 8
\]
This is a contradiction, so there are **no solutions**.
2. **Equation 2:** \( -8x + 3 = -8x + 3 \)
This simplifies to:
\[
0 = 0
\]
This statement is always true, meaning there are **infinitely many solutions**.
3. **Equation 3:** \( -3x + 8 = -3x - 8 \)
Subtract \( -3x \) from both sides:
\[
8 = -8
\]
This is another contradiction, so there are **no solutions**.
4. **Equation 4:** \( -3x - 8 = 3x - 8 \)
Add \( 3x \) to both sides:
\[
-8 = 6x - 8
\]
Adding \( 8 \) to both sides:
\[
0 = 6x \implies x = 0
\]
This equation has **exactly one solution**: \( x = 0 \).
From this analysis, the equation that has exactly one solution is:
**Answer: \( -3x - 8 = 3x - 8 \)**.
1. **Equation 1:** \( 3x - 8 = 3x + 8 \)
Subtract \( 3x \) from both sides:
\[
-8 = 8
\]
This is a contradiction, so there are **no solutions**.
2. **Equation 2:** \( -8x + 3 = -8x + 3 \)
This simplifies to:
\[
0 = 0
\]
This statement is always true, meaning there are **infinitely many solutions**.
3. **Equation 3:** \( -3x + 8 = -3x - 8 \)
Subtract \( -3x \) from both sides:
\[
8 = -8
\]
This is another contradiction, so there are **no solutions**.
4. **Equation 4:** \( -3x - 8 = 3x - 8 \)
Add \( 3x \) to both sides:
\[
-8 = 6x - 8
\]
Adding \( 8 \) to both sides:
\[
0 = 6x \implies x = 0
\]
This equation has **exactly one solution**: \( x = 0 \).
From this analysis, the equation that has exactly one solution is:
**Answer: \( -3x - 8 = 3x - 8 \)**.