This image contains a math problem with several parts. Here's a breakdown of the first equation (solving for X) and the options for which equation has no solution.

Solving for X:

The first equation given is: $4(3x - 2) + 5 = 2(5x + 1) + 3x$ You have already started solving this equation:

1. Distribute the terms: $12x - 8 + 5 = 10x + 2 + 3x$
2. Combine like terms: $12x - 3 = 13x + 2$
3. Move all terms involving $x$ to one side and constant terms to the other side: $12x - 13x = 2 + 3$ $- x = 5$
4. Solve for $x$: $x = -5$

Question 2: Which equation has no solution?

Now, let’s evaluate the options to identify the one with no solution.

• A) $3x + 1 = 3x - 1$

  • Simplifying both sides, we get $1 = -1$, which is impossible, so this has no solution.

• B) $3x - 1 = x + 3$

  • Solving this gives $2x = 4$, so $x = 2$. This has a solution.

• C) $3 - x = -3x$

  • Solving this gives $3 = -2x$, so $x = -\frac{3}{2}$. This has a solution.

• D) $3x = 3x$

  • This is true for all values of $x$, so it has infinitely many solutions.

Thus, A) is the equation with no solution.

Would you like me to explain anything in more detail? Here are some additional related questions:

1. How do you solve linear equations that have terms on both sides?
2. What does it mean when an equation has no solution?
3. How can you check if an equation has infinitely many solutions?
4. How do you recognize and solve equations with fractions or decimals?
5. Can an equation have one solution, no solution, or infinitely many solutions?

Tip: Always combine like terms first to simplify your equations before isolating the variable.