Solving Linear Equations Quick Check

2 of 52 of 5 Items

Question
Using the properties of equality, find the solution to the equation 2f5−85+2f=8 .(1 point)
Responses

166
Start Fraction 16 over 6 End Fraction

83
Start Fraction 8 over 3 End Fraction

12
12

4
4

1 answer

To solve the equation \(2f5 - 85 + 2f = 8\), we first need to rewrite it in a clearer format.

However, it seems you might have a typo with "2f5." I'll assume you meant to write "2f" that is multiplied by "5," making the equation look like this:

\[ 2f \cdot 5 - 85 + 2f = 8 \]

Let's simplify it step by step:

  1. Distribute \(2f \cdot 5\):

\[ 10f - 85 + 2f = 8 \]

  1. Combine like terms (\(10f\) and \(2f\)):

\[ 12f - 85 = 8 \]

  1. Add 85 to both sides:

\[ 12f = 8 + 85 \] \[ 12f = 93 \]

  1. Divide both sides by 12 to isolate \(f\):

\[ f = \frac{93}{12} \]

  1. Simplify the fraction \( \frac{93}{12} \):

\[ f = \frac{31}{4} = 7.75 \quad \text{(or 7 and 3/4)} \]

Since none of the provided responses match \(7.75\), let's confirm whether the options align better with the fraction form.

Con 1: \( 16/6 = 8/3 \) Con 2: \( 31/4 \)

None of the available choices are exact, but it seems the correct answer is \( \frac{31}{4} \), or if approximated, \( 7.75 \).

Based on the nearest simplified fraction available as a response, although none match perfectly, the closest choices do not match correctly with the answer derived from \(2f5 - 85 + 2f = 8\).

Please ensure the equation was written correctly for the answer selection to be appropriate.

If \(2f5\) was indeed meant to refer to a specific value or other operator, please clarify.

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