Question

Please help with this question. Ignore my current answer selection, it's not correct.

Answer 1

Choice b is correct.

Explanation:

We have given an inequality:

`(12)/(25)-(3b)/(10) <(1)/(2)-(b)/(5)`

We have to solve this inequality.

`(12)/(25)-(3b)/(10) <(1)/(2)-(b)/(5)`

`(2(12)-5(3b))/(50)<(5-2b)/(10)`

`10(24-15b)<50(5-2b)`

240-150b < 250-100b

240-250 < -100b+150b

-10 < 50b

b > -1/5 is the answer.

Answer 2

`b\:>\:-(1)/(5)`

Explanation:

The given inequality is

`(12)/(25) -(3b)/(10)\:<\:(1)/(2)-(b)/(5)`

Multiply through by 50.

`2(12) -5(3b)\:<\:25(1)-10(b)`

Simplify;

`24-15b\:<\:25-10b`

Group like terms

`24-25\:<\:-10b+15b`

`-1\:<\:5b`

Divide both sides of the inequality by 5.

`-(1)/(5)\:<\:b`

`b\:>\:-(1)/(5)`