Which of the following is an example of an equation with no solution?(1 point)
Responses
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
4x+3=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
3x+4=4x+3
3x+4=4x+3 is an example of an equation with no solution.
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
4x+3=4x+3
4 x plus 3 equals 4 x plus 3
3x+4=3x+3
Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x (1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=3.
The equation has one solution: x equals 3 .
Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15 (1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
The equation has no solution.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=−10.
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6 (1 point)
Responses
The equation has one solution: x=10.
The equation has one solution: x equals 10 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=6.
The equation has one solution: x equals 6 .
The equation has no solution.
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To determine which of the given equations has no solution, we need to simplify them and compare the coefficients of the variable (x). If the coefficients are the same on both sides of the equation, it means the equation has infinitely many solutions. However, if the coefficients are different, it means the equation has no solution.
Let's apply this process to each equation:
1) 3x + 4 = 3x + 3
Simplifying the equation, we see that the coefficient of x on both sides is 3, so this equation has infinitely many solutions.
2) 4x + 3 = 3x + 3
Simplifying the equation, we see that the coefficient of x on the left side is 4, while on the right side it is 3. Since the coefficients are different, this equation has no solution.
3) 3x + 4 = 3x + 4
Simplifying the equation, we see that the coefficient of x on both sides is 3, so this equation has infinitely many solutions.
4) 3x + 4 = 4x + 3
Simplifying the equation, we see that the coefficient of x on the left side is 3, while on the right side it is 4. Since the coefficients are different, this equation has no solution.
Therefore, the equation with no solution is 4x + 3 = 3x + 3.