SOLUTION: 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

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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(52784)   (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.


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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(20850)   (Show Source): You can put this solution on YOUR website!

.....1)
.....2)
-----------------------------
.....2)


.....1).........substitute in 2)






the following could be a value of
B.



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.
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