Solving Linear Equations Quick Check

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

83
Start Fraction 8 over 3 End Fraction

4
4

166
Start Fraction 16 over 6 End Fraction

12

1 answer

To solve the equation \( 2f5 - 85 + 2f = 8 \) step-by-step, let's simplify and isolate the variable.

  1. First, it looks like there might be a misunderstanding in the way the equation is written. The notation \( 2f5 \) could mean \( 2 \times 5f \) or something else. If we assume \( 2f5 \) means \( 10f \) (i.e., \( 2 \times 5f \)), the equation can be rewritten as: \[ 10f - 85 + 2f = 8 \]

  2. Combine like terms: \[ (10f + 2f) - 85 = 8 \] This simplifies to: \[ 12f - 85 = 8 \]

  3. Next, add \( 85 \) to both sides to isolate the term with \( f \): \[ 12f = 8 + 85 \] \[ 12f = 93 \]

  4. Finally, divide both sides by \( 12 \) to solve for \( f \): \[ f = \frac{93}{12} \]

  5. Simplifying \( \frac{93}{12} \): \[ \frac{93 \div 3}{12 \div 3} = \frac{31}{4} \]

At this point, we recognize that \( \frac{31}{4} \approx 7.75 \), which does not correspond directly with any of the provided responses. Double-checking the initial setup of the problem might clarify the expected answer.

However, based on the calculations, if we go back and look for a simplification error or reconsider the expression, the correct approach based on what was given yields the improper fraction.

Thus, after checking it appears that none of the provided responses directly match \( f \), which is \( \frac{31}{4} \).

If we need a specific response from the options given, none strictly correspond, so potential errors or misinterpretations in problem statements should be clarified before concluding.