Question 1183473: b <= 2a - 1
8 > a - b
According to the system of inequalities above, which of the following could be a value of a?
A. - 12
B. - 8
C. - 7
D. - 6
Found 3 solutions by ikleyn, MathLover1, greenestamps:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! b <= 2a - 1
8 > a - b
According to the system of inequalities above, which of the following could be a value of a?
A. - 12
B. - 8
C. - 7
D. - 6
~~~~~~~~~~~~
You are given two inequalities
b <= 2a - 1 (1)
and
8 > a - b. (2)
This system of inequalities is equivalent to
b <= 2a - 1 (3)
b > a - 8 (4)
From (3) and (4), you have
a - 8 < b <= 2a - 1,
which implies
a - 8 < 2a - 1. (5)
Subtracting "a" from both sides of (5), you get
- 8 < a - 1,
or
- 8 + 1 < a,
a > -7.
Having it, you see that options A), B) and C) do not work.
The option D) works.
Solved, answered and explained.
/\/\/\/\/\/\/\/
The solution by @MathLover1 has an error, and her answer is incorrect.
The error is in the 9-th line from the top. Be aware.
Answer by MathLover1(20849)  (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Rewrite the second inequality as
a < b+8
Then note that the phrasing of the question implies that exactly one of the answer choices is correct.
Since "a < b+8" has to be true for only one of the answer choices, the answer has to be the largest (least negative) of the choices. So the answer has to be D, -6.
For a correct algebraic solution to the problem, see the response from tutor @ikleyn.
|
|
|
