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Which of the following equations have no solutions?

Choose all answers that apply:
A. [tex]29x - 29 = 29x - 11[/tex]
B. [tex]29x + 11 = 29x - 11[/tex]
C. [tex]29x + 29 = 29x - 11[/tex]
D. [tex]29x + 92 = 29x - 11[/tex]

Sagot :

GinnyAnswer
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]
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