Answer:
The value of the fraction [tex]\dfrac{7-2y}{6}[/tex] greater than the value of the fraction [tex]\dfrac{3y-7}{12}[/tex] for [tex]y<3.[/tex]
Step-by-step explanation:
Find for which values the fraction [tex]\dfrac{7-2y}{6}[/tex] is greater than the fraction [tex]\dfrac{3y-7}{12}.[/tex]
Solve the inequality:
[tex]\dfrac{7-2y}{6}>\dfrac{3y-7}{12}[/tex]
Multiply it by 12:
[tex]2(7-2y)>3y-7\\ \\14-4y>3y-7[/tex]
Separate variables and numbers:
[tex]-4y-3y>-7-14\\ \\-7y>-21[/tex]
Divide by -7:
[tex]y<3[/tex]
The value of the fraction [tex]\dfrac{7-2y}{6}[/tex] greater than the value of the fraction [tex]\dfrac{3y-7}{12}[/tex] for [tex]y<3.[/tex]
