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: \[ 3x + 4 - 3x = 3 \ 4 = 3 \] This is a contradiction, indicating no solutions.

B. \(3x + 4 = 4x + 3\)

When we simplify: \[ 3x + 4 - 4x = 3 \ 4 - 3 = x \ 1 = x \] 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!