Justify why −12(x−3)−52=−16 has one solution, infinitely many solutions, or no solution.(1 point) Responses 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=0. It has one solution because the solution is in the form x equals a . The solution is x equals 0 . It has one solution, because the solution is in the form x=a. The solution is x=−12.

Question

Justify why −12(x−3)−52=−16 has one solution, infinitely many solutions, or no solution.(1 point) Responses 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=0. It has one solution because the solution is in the form x equals a . The solution is x equals 0 . It has one solution, because the solution is in the form x=a. The solution is x=−12.

Answer 1

To solve the equation, we need to simplify the left side first:

-12(x-3)-52 = -16
-12x + 36 - 52 = -16
-12x - 16 = -16
-12x = 0

Now, to find the value of x that satisfies this equation, we divide both sides by -12:

x = 0

So, the equation has one solution, x = 0. Therefore, the correct response is: It has one solution because the solution is in the form x=a. The solution is x=0.