Which of the following is an example of an equation with no solution?
A. 4x+3=3x+3
B. 3x+4=4x+3
C. 3x+4=3x+4
D. 3x+4=3x+3
The correct answer is D. 3x+4=3x+3. This equation has no solution because when 4 is subtracted from both sides, it results in 3=3, which is true. This means that no matter the value of x, the equation will always be true and thus have no solution.
To determine which of the given equations has no solution, we need to simplify each equation and check if the variable cancels out.
A. 4x+3=3x+3
Subtracting 3x from both sides, we get:
4x - 3x + 3 = 3
x + 3 = 3
Subtracting 3 from both sides, we get:
x = 0
So, option A does have a solution.
B. 3x+4=4x+3
Subtracting 3x from both sides, we get:
3x - 3x + 4 = 3
4 = 3
Since 4 does not equal 3, option B does not have a solution.
C. 3x+4=3x+4
Subtracting 3x from both sides, we get:
3x - 3x + 4 = 4
4 = 4
Since 4 equals 4, option C has infinitely many solutions.
D. 3x+4=3x+3
Subtracting 3x from both sides, we get:
3x - 3x + 4 = 3
4 = 3
Since 4 does not equal 3, option D does not have a solution.
Therefore, the equation with no solution is option B: 3x+4=4x+3.