Which of the following must be true?

Rationale

4x-3=26 must be true.

To determine which equation must be true, we can isolate the variable x in each option and check if it leads to a consistent solution. The equation 4x-3=26 directly solves for x, confirming its validity.

A (4x-3=26) CORRECT

This equation can be solved by adding 3 to both sides to get 4x = 29, and then dividing by 4 to find x = 29/4. Since this equation is stated as true in the question, it must be valid by nature of the problem.

B (4x-1=26) YOUR ANSWER

Solving this equation involves adding 1 to both sides to yield 4x = 27, and then dividing by 4 gives x = 27/4. This value does not satisfy the original equation 4x-3=26, indicating that this option is not necessarily true.

C (5x-1=26) YOUR ANSWER

By adding 1 to both sides, we find 5x = 27, leading to x = 27/5. This solution does not correspond to the correct value derived from 4x-3=26. Therefore, this equation does not have to be true.

D (5x+1=26) YOUR ANSWER

To solve this, subtract 1 from both sides to get 5x = 25, which simplifies to x = 5. This does not equate to the solution of the first equation, confirming that this statement cannot be true.

Conclusion

Among the choices presented, only the equation 4x-3=26 must be true. The other options lead to values of x that do not satisfy the original equation, establishing 4x-3=26 as the sole statement that is universally valid in this context.