Answer :
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:
[tex]\frac{7-2y}{6}[/tex] and [tex]\frac{3y-7}{12}[/tex]
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:
[tex]\frac{7-2y}{6} >\frac{3y-7}{12}[/tex]
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:
[tex]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<3[/tex]
This means, for y lesser than 3, the value of first fraction is larger than the second one.