Justify why −12(x−3)−52=−16 has one solution, infinitely many solutions, or no solution.(1 point)
Responses
It has one solution because the solution is in the form x=a. The solution is x=0.
It has one solution because the solution is in the form x equals a . The solution is x equals 0 .
It has infinitely many solutions because the solution is in the form a=a.
It has infinitely many solutions because the solution is in the form a equals a .
It has no solution because the solution is in the form a=b.
It has no solution because the solution is in the form a equals b .
It has one solution, because the solution is in the form x=a. The solution is x=−12.
None of the given responses are correct.
To determine the number of solutions, we need to simplify the equation and check if the result is true or false.
Starting with the given equation: -12(x-3) - 52 = -16
First, distribute -12 to the terms inside the parentheses:
-12*x + 36 - 52 = -16
Combine like terms:
-12*x - 16 = -16
Next, add 16 to both sides of the equation to isolate the variable:
-12*x = 0
Now, divide both sides of the equation by -12 to solve for x:
x = 0
Since the result of the equation is x = 0, we can conclude that it has one solution.