Complete the equation so that it has infinite solutions.(1 point)
4x+10= ____________x+ ___________
4x+10=4x+10
Complete the equation so that it has no solution.(1 point)
5x+12= _____________x+9
5x+12=5x+9
Complete the equation so that it has no solution.(1 point)
−7x−12= ____x+12
−7x−12= -7x+12
Solve for x to determine if the equation has one, none, or infinite solutions.
6(2x+4)−24=12x
(1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−20.
The equation has one solution: x equals negative 20 .
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has no solution.
To determine if the equation has one, none, or infinite solutions, we need to solve for x:
6(2x + 4) - 24 = 12x
12x + 24 - 24 = 12x
12x = 12x
This equation simplifies to 0 = 0, which means it is always true. This indicates that there are an infinite number of solutions. So, the correct option is:
The equation has infinite solutions.