Question

Solving Linear Equations Quick Check
2 of 52 of 5 Items




Question
Using the properties of equality, find the solution to the equation 2f/5−8/5+2f=8 .(1 point)
Responses

16/6


8/3



12


4

Answer 1

To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we can first eliminate the fractions by multiplying the entire equation by 5:

\[
5\left(\frac{2f}{5}\right) - 5\left(\frac{8}{5}\right) + 5(2f) = 5(8)
\]

This simplifies to:

\[
2f - 8 + 10f = 40
\]

Now combine the like terms (\(2f\) and \(10f\)):

\[
12f - 8 = 40
\]

Next, add 8 to both sides to isolate the term with \(f\):

\[
12f = 48
\]

Now, divide both sides by 12:

\[
f = \frac{48}{12} = 4
\]

The solution is \( f = 4 \).

Thus, the correct response is **4**.