Question

Please help with the problem below! Thank you

Answer 1

Choice A is correct. d ≤ -3 is the answer.

Explanation:

We have given an inequality:

`(d-3)/(10)\geq (2d+3)/(5)+(d+3)/(5)`

We have to solve the inequality.

`(d-3)/(10)\geq (3(2d+3)+5(d+3))/(15)=(6d+9+5d+15)/(15)=(11d+24)/(15)`

`(d-3)/(10)\geq (11d+24)/(15)`

`15(d-3)\geq10(11d+24)`

`15d-45\geq110d+240`

15d-110d ≥ 240+45

-95d ≥ 285

d ≤ -3 which is the answer.

Answer 2

`d \le -3`

Explanation:

The given inequality is;

`(d-3)/(10) \ge (2d+3)/(5)+(d+3)/(3)`

Clear the fraction by multiply through by 30;

`3(d-3) \ge 6(2d+3)+10(d+3)`

Expand;

`3d-9\ge 12d+18+10d+30`

Group like terms;

`3d-12d-10d \ge 18+30+9`

`-19d \ge 57`

Divide through by -19 and reverse the sign.

`d \le -3`