Which of the following is an example of an equation with no solution?(1 point)
a:3x+4=3x+4
b:3x+4=4x+3
c:3x+4=3x+3
d:4x+3=3x+3
c: 3x+4=3x+3
To determine which equation has no solution, we need to compare the coefficients of the variables on both sides of the equation.
a: 3x+4=3x+4
The coefficients on both sides of the equation are the same (3x). Therefore, this equation has infinitely many solutions.
b: 3x+4=4x+3
In this equation, the coefficients are different: 3x on the left side and 4x on the right side.
To eliminate the variable, we can subtract 3x from both sides of the equation: 3x+4-3x=4x+3-3x. Simplifying this, we get 4=4x+3-3x, which simplifies further to 4=x+3.
To isolate the variable, we subtract 3 from both sides: 4-3=x+3-3, which simplifies to 1=x.
Therefore, this equation does have a solution, which is x=1.
c: 3x+4=3x+3
Here, the variables have the same coefficient on both sides. By subtracting 3x from both sides of the equation: 3x+4-3x=3x+3-3x, we get 4=3, which is not true.
Therefore, this equation has no solution.
d: 4x+3=3x+3
In this equation, the coefficients on both sides of the equation are the same (4x and 3x). To eliminate the variable, we can subtract 3x from both sides of the equation: 4x+3-3x=3x+3-3x. This simplifies to x+3=3.
To isolate the variable, we subtract 3 from both sides: x+3-3=3-3. This further simplifies to x=0.
Therefore, this equation does have a solution, which is x=0.
So, the equation with no solution is c: 3x+4=3x+3.