To determine which of the given equations have no solutions, we will compare both sides of each equation step-by-step and check if any contradictions arise.
Equation A: \( 29x - 29 = 29x - 11 \)
1. Subtract \( 29x \) from both sides:
[tex]\[ -29 = -11 \][/tex]
2. This simplifies to:
[tex]\[ -29 \neq -11 \][/tex]
Since this is a contradiction, there are no solutions for Equation A.
Equation B: \( 29x + 11 = 29x - 11 \)
1. Subtract \( 29x \) from both sides:
[tex]\[ 11 = -11 \][/tex]
2. This simplifies to:
[tex]\[ 11 \neq -11 \][/tex]
Since this is a contradiction, there are no solutions for Equation B.
Equation C: \( 29x + 29 = 29x - 11 \)
1. Subtract \( 29x \) from both sides:
[tex]\[ 29 = -11 \][/tex]
2. This simplifies to:
[tex]\[ 29 \neq -11 \][/tex]
Since this is a contradiction, there are no solutions for Equation C.
Equation D: \( 29x + 92 = 29x - 11 \)
1. Subtract \( 29x \) from both sides:
[tex]\[ 92 = -11 \][/tex]
2. This simplifies to:
[tex]\[ 92 \neq -11 \][/tex]
Since this is a contradiction, there are no solutions for Equation D.
Hence, all the given equations (A, B, C, and D) have no solutions.
The answers are:
- A) \( 29x - 29 = 29x - 11 \)
- B) \( 29x + 11 = 29x - 11 \)
- C) \( 29x + 29 = 29x - 11 \)
- D) [tex]\( 29x + 92 = 29x - 11 \)[/tex]
