Which of the following is an example of an equation with exactly one solution?

Question

A. 3x + 4 = 3x + 3
B. 3x + 4 = 4x + 3
C. 4x + 3 = 4x + 3
D. 3x + 4 = 3x + 4

Answer 1

To determine which equation has exactly one solution, we can analyze each of the options.

A. $3x+4=3x+3$

Subtract $3x$ from both sides: $$4=3$$ This is a false statement, indicating no solutions.

B. $3x+4=4x+3$

Subtract $3x$ from both sides: $$4=x+3$$ Subtract 3 from both sides: $$1=x$$ This means there is exactly one solution: $x=1$.

C. $4x+3=4x+3$

This simplifies to: $$0=0$$ This is a true statement for all $x$, indicating infinitely many solutions.

D. $3x+4=3x+4$

Similar to option C, this simplifies to: $$0=0$$ Indicating infinitely many solutions.

From this analysis, the only equation with exactly one solution is:

B. $3x+4=4x+3$.

Answer 2

are you sure this is correct

Answer 3

Yes, I am confident in the analysis of the equations provided. Let’s briefly revisit each option to clarify:

A. $3x+4=3x+3$

When we simplify: $$3x+4-3x=34=3$$ This is a contradiction, indicating no solutions.

B. $3x+4=4x+3$

When we simplify: $$3x+4-4x=34-3=x1=x$$ This results in exactly one solution: $x=1$.

C. $4x+3=4x+3$

This simplifies to: $$0=0$$ This is always true for any value of $x$, indicating infinitely many solutions.

D. $3x+4=3x+4$

Similar to C, this also simplifies to: $$0=0$$ Again indicating infinitely many solutions.

Therefore, the only equation that has exactly one solution is indeed:

B. $3x+4=4x+3$.

If there’s any confusion or further questions about this, feel free to ask!