Question

witch of the following is an example of an equation with exactly on solution

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

Answer 1

To determine which of the equations has exactly one solution, let's analyze each option:

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

Subtract \( 3x \) from both sides:
\[
4 = x + 3
\]
Subtract 3 from both sides:
\[
1 = x \quad \text{(One solution: } x = 1\text{)}
\]

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

Subtract \( 3x \) from both sides:
\[
4 = 3 \quad \text{(No solution, a contradiction)}
\]

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

Subtract \( 3x \) from both sides:
\[
x + 3 = 3
\]
Subtract 3 from both sides:
\[
x = 0 \quad \text{(One solution: } x = 0\text{)}
\]

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

This simplifies to:
\[
0 = 0 \quad \text{(Infinitely many solutions)}
\]

So, the equations with exactly one solution are A (\( x = 1 \)) and C (\( x = 0 \)).

If you are looking for just one equation, both A and C qualify, but since the question asks for one, you can accept either A or C as correct.

Final answers:
**A. 3x + 4 = 4x + 3** or **C. 4x + 3 = 3x + 3** each have exactly one solution.