To solve this equation, we have to isolate the variable f, or get it alone on one side of the equation.
1/7f - 5 1/2 = 9/14
To do this, we need to add 5 1/2 to both sides of the equation to 1) cancel out the - 5 1/2 on the left side of the equation, and 2) maintain equality both sides of the equation.
1/7f - 5 1/2 + 5 1/2 = 9/14 + 5 1/2
1/7f = 6 2/14
Next, we have to divide both sides by 1/7, to get rid of the coefficient of f on the left side of the equation.
1/7f ÷ 1/7 = 6 2/14 ÷ 1/7
f = 43
Therefore, the the value of f is 43.