Which of the following equations has no real solutions? A. 3x-3=3x-3 B 3(x+3)=3(x+13) C 3(x-3)=3x-9 D. 3x-3=9x-3

To determine which equation has no real solutions, we need to analyze each equation and see if it leads to a contradiction.

A. $3x - 3 = 3x - 3$

Subtract $3x$ from both sides:
$$-3 = -3$$

This is a true statement and holds for all values of $x$. Therefore, this equation has infinitely many solutions.

B. $3(x + 3) = 3(x + 13)$

Expand both sides:
$$3x + 9 = 3x + 39$$

Subtract $3x$ from both sides:
$$9 = 39$$

This is a contradiction, meaning there are no real solutions for this equation.

C. $3(x - 3) = 3x - 9$

Expand the left side:
$$3x - 9 = 3x - 9$$

Subtract $3x$ from both sides:
$$-9 = -9$$

This is a true statement and holds for all values of $x$. Therefore, this equation has infinitely many solutions.

D. $3x - 3 = 9x - 3$

Subtract $3x$ from both sides:
$$-3 = 6x - 3$$

Add 3 to both sides:
$$0 = 6x$$

Divide by 6:
$$x = 0$$

This equation has one solution, $x = 0$.

Therefore, the equation that has no real solutions is:

B. $3(x + 3) = 3(x + 13)$