Question
Justify why −12(x−3)−52=−16 has one solution, infinitely many solutions, or no solution.
1.It has no solution because the solution is in the form a=b.
2.t has infinitely many solutions because the solution is in the form a=a.
3.It has one solution because the solution is in the form x=a. The solution is x=0.
4.It has one solution, because the solution is in the form x=a. The solution is x=−12.
1.It has no solution because the solution is in the form a=b.
2.t has infinitely many solutions because the solution is in the form a=a.
3.It has one solution because the solution is in the form x=a. The solution is x=0.
4.It has one solution, because the solution is in the form x=a. The solution is x=−12.
Answers
GPT 3.5
The correct answer is 3. It has one solution because the solution is in the form x=a. The solution is x=0.
To justify this, we can simplify the equation −12(x−3)−52=−16 and solve for x.
First, distribute the -12 to the terms inside the parentheses:
-12(x-3) - 52 = -16
-12x + 36 - 52 = -16
Combine like terms:
-12x - 16 = -16
Next, isolate the variable by adding 16 to both sides:
-12x = 0
Finally, divide both sides by -12 to solve for x:
x = 0
So the equation has one solution, x = 0.
To justify this, we can simplify the equation −12(x−3)−52=−16 and solve for x.
First, distribute the -12 to the terms inside the parentheses:
-12(x-3) - 52 = -16
-12x + 36 - 52 = -16
Combine like terms:
-12x - 16 = -16
Next, isolate the variable by adding 16 to both sides:
-12x = 0
Finally, divide both sides by -12 to solve for x:
x = 0
So the equation has one solution, x = 0.