IDNLearn.com makes it easy to get reliable answers from knowledgeable individuals. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.
Sagot :
Let's analyze each of the equations step-by-step to determine the nature of their solutions.
### Equation A: \( 6 + 3x = 3x - 3 \)
1. Initial equation:
[tex]\[ 6 + 3x = 3x - 3 \][/tex]
2. Subtract \(3x\) from both sides:
[tex]\[ 6 + 3x - 3x = 3x - 3 - 3x \][/tex]
3. Simplify:
[tex]\[ 6 = -3 \][/tex]
The statement \(6 = -3\) is a contradiction, indicating there is no solution for Equation A. Therefore, Equation A has no solution.
### Equation B: \( 2(4x - 1) = 8x - 2 \)
1. Distribute the 2 on the left-hand side:
[tex]\[ 2 \cdot 4x - 2 \cdot 1 = 8x - 2 \][/tex]
2. Simplify:
[tex]\[ 8x - 2 = 8x - 2 \][/tex]
This simplifies to an identity, which is \( 8x - 2 = 8x - 2 \). Since both sides of the equation are always equal regardless of the value of \( x \), Equation B has an infinite number of solutions.
### Summary of the Solutions:
- Equation A has no solution.
- Equation B has an infinite number of solutions.
### Verify the Given Statements:
1. Equation \( A \) and Equation \( B \) have an infinite number of solutions.
- This is false because Equation A has no solution.
2. Equation \( A \) has no solution and Equation \( B \) has an infinite number of solutions.
- This is true.
3. Equation \( A \) has an infinite number of solutions and Equation \( B \) has no solution.
- This is false because it is the reverse of the actual solution.
4. Equation \( A \) and Equation \( B \) have no solution.
- This is false because Equation B has an infinite number of solutions.
Based on the above analysis, the true statement is:
Equation \( A \) has no solution and Equation \( B \) has an infinite number of solutions.
Thus, the correct answer is 2.
### Equation A: \( 6 + 3x = 3x - 3 \)
1. Initial equation:
[tex]\[ 6 + 3x = 3x - 3 \][/tex]
2. Subtract \(3x\) from both sides:
[tex]\[ 6 + 3x - 3x = 3x - 3 - 3x \][/tex]
3. Simplify:
[tex]\[ 6 = -3 \][/tex]
The statement \(6 = -3\) is a contradiction, indicating there is no solution for Equation A. Therefore, Equation A has no solution.
### Equation B: \( 2(4x - 1) = 8x - 2 \)
1. Distribute the 2 on the left-hand side:
[tex]\[ 2 \cdot 4x - 2 \cdot 1 = 8x - 2 \][/tex]
2. Simplify:
[tex]\[ 8x - 2 = 8x - 2 \][/tex]
This simplifies to an identity, which is \( 8x - 2 = 8x - 2 \). Since both sides of the equation are always equal regardless of the value of \( x \), Equation B has an infinite number of solutions.
### Summary of the Solutions:
- Equation A has no solution.
- Equation B has an infinite number of solutions.
### Verify the Given Statements:
1. Equation \( A \) and Equation \( B \) have an infinite number of solutions.
- This is false because Equation A has no solution.
2. Equation \( A \) has no solution and Equation \( B \) has an infinite number of solutions.
- This is true.
3. Equation \( A \) has an infinite number of solutions and Equation \( B \) has no solution.
- This is false because it is the reverse of the actual solution.
4. Equation \( A \) and Equation \( B \) have no solution.
- This is false because Equation B has an infinite number of solutions.
Based on the above analysis, the true statement is:
Equation \( A \) has no solution and Equation \( B \) has an infinite number of solutions.
Thus, the correct answer is 2.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.