Question: Which of the following is the simplified inequality for 2 - 5(2 + c) ≤ 28 - c?

A ) c ≥ 9
B ) c ≥ - 9
C ) c ≤ - 9
D ) c ≤ 9

Steps to derive

 [Original inequality.]
1 2 - 5(2 + c) ≤ 28 - c

 [Use distributive property.]
2 2 - 10 - 5c ≤ 28 - c

 [Simplify.]
3 - 8 - 5c ≤ 28 - c

 [Add 8 to each side.]
4 - 8 - 5c + 8 ≤ 28 - c + 8

 [Simplify.]
5 - 5c ≤ 36 - c

 [Add c to both sides.]
6 - 5c + c ≤ 36 - c + c

 [Simplify.]
7 - 4c ≤ 36

 [Divide each side by - 4 and reverse the inequality.]
8 - 4c- 4 ≥ 36- 4

 [Simplify.]
9 c ≥ - 9



Hence the right answer is Option B

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