Question

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

Answer 1

To find the solution to the equation 2/f/5 − 8/5 + 2f = 8, we can simplify the equation using the properties of equality.

First, let's determine the LCD (Least Common Denominator) for the fractions in the equation. In this case, the LCD is 5f because the terms involve both f and 5.

Now, multiply each term by the LCD to clear the fractions:

2/f/5 * 5f - 8/5 * 5f + 2f * 5f = 8 * 5f

The f's in 2/f/5 * 5f cancel out, leaving us with 2 * 5 = 10:

10 - 8 * 5f + 2f * 5f = 40f

Expanding the terms:

10 - 40f + 10f^2 = 40f

Rearranging the terms:

10f^2 - 40f + 40f - 10 = 0

Simplifying:

10f^2 - 10 = 0

Now divide both sides of the equation by 10:

f^2 - 1 = 0

Rearranging the terms:

f^2 = 1

Taking the square root of both sides:

f = ±√1

Therefore, the solutions to the equation 2/f/5 − 8/5 + 2f = 8 are f = 1 and f = -1.