Question

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

Answer 1

are you sure this is correct

Answer 2

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 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!