To identify which of the given equations have no solutions, let's examine each equation individually by isolating the variable [tex]\( x \)[/tex].
### Equation A: [tex]\( 33x - 33 = 33x + 25 \)[/tex]
1. Subtract [tex]\( 33x \)[/tex] from both sides to isolate the constants:
[tex]\[ 33x - 33 - 33x = 33x + 25 - 33x \][/tex]
[tex]\[ -33 = 25 \][/tex]
2. This simplifies to a contradiction:
[tex]\[ -33 \neq 25 \][/tex]
Therefore, there is no solution for Equation A.
### Equation B: [tex]\( 33x + 33 = 33x + 25 \)[/tex]
1. Subtract [tex]\( 33x \)[/tex] from both sides to isolate the constants:
[tex]\[ 33x + 33 - 33x = 33x + 25 - 33x \][/tex]
[tex]\[ 33 = 25 \][/tex]
2. This simplifies to a contradiction:
[tex]\[ 33 \neq 25 \][/tex]
Therefore, there is no solution for Equation B.
### Equation C: [tex]\( 33x + 25 = 33x + 25 \)[/tex]
1. Subtract [tex]\( 33x \)[/tex] from both sides to isolate the constants:
[tex]\[ 33x + 25 - 33x = 33x + 25 - 33x \][/tex]
[tex]\[ 25 = 25 \][/tex]
2. This is a true statement:
[tex]\[ 25 = 25 \][/tex]
Therefore, Equation C is always true and has infinitely many solutions.
### Equation D: [tex]\( 33x - 25 = 33x + 25 \)[/tex]
1. Subtract [tex]\( 33x \)[/tex] from both sides to isolate the constants:
[tex]\[ 33x - 25 - 33x = 33x + 25 - 33x \][/tex]
[tex]\[ -25 = 25 \][/tex]
2. This simplifies to a contradiction:
[tex]\[ -25 \neq 25 \][/tex]
Therefore, there is no solution for Equation D.
In summary, the equations that have no solutions are:
- [tex]\( \text{A} \)[/tex]
- [tex]\( \text{B} \)[/tex]
- [tex]\( \text{D} \)[/tex]
So, the equations with no solutions are A, B, and D.
