If w>4, which of the following has the smallest value?
4/w+2
w-1/4
w+1/w
4/w-1
w+2/4
I think its the 1st answer but i'm not sure.
just solve the inequalities to see which has the smallest solution.
remember that for fractions, a larger denominator means a smaller quotient. So, for example,
if w>4, w+2 > 6, so
4/(w+2) < 4/6 = 2/3
reason similarly for the others.
To compare the values and find the smallest one, we need to substitute the value of w that satisfies the condition w > 4 into each of the given expressions.
Let's evaluate each expression using w = 5, which is greater than 4, and compare the results.
Expression 1: 4/w + 2
Substituting w = 5: 4/5 + 2 = 12/5
Expression 2: w - 1/4
Substituting w = 5: 5 - 1/4 = 19/4
Expression 3: w + 1/w
Substituting w = 5: 5 + 1/5 = 26/5
Expression 4: 4/w - 1
Substituting w = 5: 4/5 - 1 = -1/5
Expression 5: (w + 2)/4
Substituting w = 5: (5 + 2)/4 = 7/4
Now, comparing the results, we can see that the smallest value is -1/5, which corresponds to Expression 4: 4/w - 1.
Therefore, the answer is 4/w - 1.