Question

For what values of b is the difference between the fractions 2b-1/2 and 1+5b/4 negative?

Answer 1

b > -3

Explanation:

You are given two fractions:

`(2b-1)/(2)\ \text{and }\ (1+5b)/(4)`

Find the difference of these two fractions:

`(2b-1)/(2)-(1+5b)/(4)\\ \\=(2(2b-1)-(1+5b))/(4)\\ \\=(4b-2-1-5b)/(4)\\ \\=(-b-3)/(4)`

Now, find the values of bfor which the difference between the fractions is negative. Solve the inequality:

`(-b-3)/(4)<0\\ \\-b-3<0\\ \\-b<3\\ \\b>-3`