Using the properties of equality, find the solution to the equation 2f/5-8/5+2f=8

Answer 1

To solve this equation, we need to simplify and isolate the variable f.

First, let's start by combining like terms on the left side of the equation:
2f/5 + 2f = 8 + 8/5

To add the fractions, we need to find a common denominator:
The common denominator is 5. So we multiply the numerator and denominator of the second fraction (8/5) by 5:
2f/5 + 2f = 8 + (8/5) * (5/5)
2f/5 + 2f = 8 + 40/5
2f/5 + 2f = 8 + 8
2f/5 + 2f = 16

Now we have:
2f/5 + 2f = 16

To eliminate the fraction, we can multiply every term by 5:
5 * (2f/5) + 5 * (2f) = 5 * 16
2f + 10f = 80
12f = 80

Now, divide both sides of the equation by 12 to solve for f:
f = 80/12
f = 20/3

Therefore, the solution to the equation is f = 20/3.