Question

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

Answer 1

Answer:

b > -3

Step-by-step explanation:

You are given two fractions:

$\dfrac{2b-1}{2}\ \text{and }\ \dfrac{1+5b}{4}$

Find the difference of these two fractions:

$\dfrac{2b-1}{2}-\dfrac{1+5b}{4}\\ \\=\dfrac{2(2b-1)-(1+5b)}{4}\\ \\=\dfrac{4b-2-1-5b}{4}\\ \\=\dfrac{-b-3}{4}$

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

$\dfrac{-b-3}{4}<0\\ \\-b-3<0\\ \\-b<3\\ \\b>-3$