Question

witch of the following is an example of an equation with no solution

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

Answer 1

To identify which of the equations has no solution, let's analyze each option:

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

Subtracting \( 3x \) from both sides:
\[ 4 = x + 3 \]
Subtracting 3 from both sides gives:
\[ 1 = x \]
This equation has a solution: \( x = 1 \).

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

Subtracting \( 3x \) from both sides:
\[ 4 = 3 \]
This is a contradiction and has no solution.

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

Subtracting \( 3x \) from both sides:
\[ x + 3 = 3 \]
Subtracting 3 from both sides gives:
\[ x = 0 \]
This equation has a solution: \( x = 0 \).

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

This is always true for any value of \( x \), so it has infinitely many solutions.

The equation with no solution is:

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