Using the properties of equality, find the solution to the equation 2f5−85+2f=8.(1 point)
Responses
83
166
12
4
To find the solution to the equation, we need to isolate the variable "f".
First, let's simplify the equation:
2f5 - 85 + 2f = 8
Combine like terms:
4f + 5 - 85 = 8
Now, simplify further:
4f - 80 = 8
Next, add 80 to both sides of the equation:
4f = 88
To isolate "f", divide both sides of the equation by 4:
f = 22
Therefore, the solution to the equation is f = 22.
The correct response is: 22
wrong
Apologies for the mistake. Let's correct it:
2f^5 - 85 + 2f = 8
First, let's combine the "f" terms:
2f^5 + 2f - 85 = 8
Next, let's subtract 8 from both sides to isolate the "f" terms:
2f^5 + 2f - 85 - 8 = 0
2f^5 + 2f - 93 = 0
Now, there is no simple way to solve this equation using the properties of equality. It is a fifth-degree polynomial equation, and its solution requires more advanced techniques such as factoring or using numerical methods.
Therefore, the correct response is that the solution to the equation cannot be found using only the properties of equality.
To find the solution to the equation 2f5 - 85 + 2f = 8, we can simplify the equation step by step using the properties of equality.
Step 1: Combine like terms
Combine the terms with the same variable, which in this case is "f".
2f + 2f = 4f
Step 2: Move the constant term
Move the constant term "85" to the right side of the equation by adding it to both sides.
4f = 8 + 85
4f = 93
Step 3: Solve for f
Divide both sides of the equation by 4 to isolate the variable f.
4f/4 = 93/4
f = 23.25
So, the solution to the equation 2f5 - 85 + 2f = 8 is f = 23.25. However, in the given response options, the closest value to 23.25 is 12.