Question

Is the value of the fraction 7−2y/6 greater than the value of the fraction 3y−7/12 ?

Answer 1

Complete Question:

Is the value of the fraction 7−2y/6 greater than the value of the fraction 3y−7/12 ?  For what values?(Make sure to use an inequality)

Answer:

y < 3

Step-by-step explanation:

The given two fractions are:

$\frac{7-2y}{6}$ and $\frac{3y-7}{12}$

We have to tell for which range of values is the value of first fraction larger than the second fraction. This can be done by setting up an inequality as shown:

$\frac{7-2y}{6} >\frac{3y-7}{12}$

The range of y which will satisfy this inequality will result in first fraction of larger value as compared to the second fraction.

Multiplying both sides of inequality by 12, we get:

$12 \times \frac{7-2y}{6} > 12 \times \frac{3y-7}{12} \\\\ 2(7-2y)>3y-7\\\\ 14-4y>3y-7\\\\ 14+7>3y+4y\\\\ 21>7y\\\\ 3>y\\\\ y$

This means, for y lesser than 3, the value of first fraction is larger than the second one.