Which of the following is an example of an equation with no solution?

Question

3x + 4 = 3x + 3
3x + 4 = 3x + 4
4x + 3 = 3x + 3
3x + 4 = 4x + 3

Answer 1

An equation with no solution occurs when simplifying the equation leads to a contradiction. Let's analyze each option:

1. 3x + 4 = 3x + 3

   Subtracting $3x$ from both sides gives: $$4=3$$ This is a contradiction. Thus, this equation has no solution.

2. 3x + 4 = 3x + 4

   Subtracting $3x$ from both sides simplifies to: $$4=4$$ This is always true for any value of $x$. Hence, this has infinitely many solutions.

3. 4x + 3 = 3x + 3

   Subtracting $3x$ from both sides gives: $$x+3=3$$ Subtracting 3 from both sides gives: $$x=0$$ This equation has a unique solution.

4. 3x + 4 = 4x + 3

   Subtracting $3x$ from both sides results in: $$4=x+3$$ Subtracting 3 from both sides gives: $$x=1$$ This equation also has a unique solution.

From this analysis, the equation that has no solution is:

3x + 4 = 3x + 3