The equation that has no solutions is the one that results in a contradiction. A contradiction is achieved when both sides of the equation are equal to different values that cannot be combined.
Analyzing each equation:
A. 6x + 3 = -6x + 3
In this equation, the variable terms cancel out on both sides, resulting in the statement 3=3. Both sides are equal, so this equation has infinitely many solutions.
B. -6x + 4 = 6x + 3
In this equation, the variable terms do not cancel out. Combining like terms, we get -6x - 6x = -1. Simplifying further, we have -12x = -1. Dividing both sides by -12, we get x = 1/12. Therefore, this equation has a solution (x = 1/12).
C. -6x + 4 = -6x + 3
In this equation, the variable terms cancel out on both sides, resulting in the statement 4 = 3. These two values are not equal, so this equation has no solution.
D. 6x + 4 = 6x + 4
In this equation, the variable terms do not cancel out. Simplifying, we get 4 = 4. Both sides of the equation are equal, so this equation has infinitely many solutions.
Therefore, the equation that has no solutions is C. -6x + 4 = -6x + 3.
Which of the following equations has no solutions?
A. 6x + 3 = -6x + 3
B. -6x + 4 = 6x + 3
C. -6x + 4 = -6x + 3
D. 6x + 4 = 6x + 4
1 answer
1 answer