If x + 12 ≤ 5 − y and 5 − y ≤ 2(x − 3), then which statement is true?
A.
x + 12 ≤ 2(5 − y)
B.
x + 12 ≤ 2x − 3
C.
x + 12 ≤ 2(x − 3)
D.
x + 12 ≤ y − 5
To solve this problem, we can start by simplifying the given inequalities:
x + 12 ≤ 5 - y can be rewritten as x ≤ 5 - y - 12 which simplifies to x ≤ -y - 7.
5 - y ≤ 2(x - 3) can be rewritten as -y ≤ 2x - 6 - 5 which simplifies to -y ≤ 2x - 11.
Now, we can compare the two inequalities to determine which statement is true.
Starting with the first inequality, x ≤ -y - 7, we can divide both sides by -1 to get y + 7 ≤ -x.
Comparing this result to the second inequality, -y ≤ 2x - 11, it is clear that y + 7 ≤ -x is more restrictive.
Therefore, the true statement is x + 12 ≤ y - 5, which can be rearranged as x + 12 ≤ 2(x - 3).
Therefore, the correct answer is C.