how can i solve this inequalities problem?

A: 6y+12/5<5y+1/4

cross multiplication

that means multiply 6y+12/5 by 4

and

multiply 5y+1/4 by 5

4(6y+12) > 5(5y+1)

=24y+48>25y+5

bring all 'y' terms on one side & numericals on another side

=48-5>25y-24y

= 43>y(answer)

2(3y+6)/5 < 5y+1/4

expand

(6y +12)/5 < 5y +1/4

multiply both sides of the inequality by 5 to get

6y +12 < 25y +5/4

substract 6y from both sides to get

12 < 25y -6y +5/4

substract 5/4 from both sides to get

12 -5/4 < 19y

(48 -5)/4 <19y

43/4 <19y

divide both sides by 19 to get

(43/4)/19 < y

43/76 < y

*************************

Note the only way to get the solution

43 < y is to solve the following equation which is different from your equation.

2(3y+6)/5< (5y+1)/4

Parentheses make a difference, use them

(6y +12)/5 < (5y +1)/4

4(6y +12) < 5(5y +1)

24y +48 < 25y +5

48 -3 < 25y -24y

43 < y

First simplify:

(6y + 12) /5 < 5y + 1/4

Multiply both sides by 5

6y + 12 < 25y + 5/4

subtract 6y from both sides

12 < 19y + 5/4

subtract 5/4 from both sides

OOps that won't work, can'T treat < like an =

sorry.

6y+12/5 < 5y/4

20(6y+12)/5 < 20(5y)/4

4(6y+12) < 5(5y)

24y+12 < 25y

= y>12