Question

Which of the following is an example of an equation with exactly one solution?
A. 3x+4=3x+3
B. 4x+3=4x+3
C. 3x+4=3x+4
D. 3x+4=4x+3

Answer 1

To determine which option has exactly one solution, let's analyze each equation:

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

Subtract \( 3x \) from both sides:

\[ 4 = 3 \]

This statement is false, meaning there are no solutions.

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

Both sides are identical, meaning this equation is true for all values of \( x \). Therefore, it has infinitely many solutions.

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

Similar to option B, both sides are identical, which means this equation is also true for all values of \( x \). Thus, it has infinitely many solutions.

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

Subtract \( 3x \) from both sides:

\[ 4 = x + 3 \]

Subtract 3 from both sides:

\[ x = 1 \]

This equation has exactly one solution: \( x = 1 \).

Therefore, the answer is **D. \( 3x + 4 = 4x + 3 \)**.