If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of a + b?
Thanks.
Max possible integer value
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-13 < 7a + 1 < 29uniyal01 wrote:If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of a + b?
Thanks.
Subtract 1:
-14 < 7a < 28
Divide by 7:
-2 < a < 4
Thus:
a < 4.
19 < 2 - b < 23
Subtract 2:
17 < -b < 21
Multiply by -1 and flip the inequalities:
-17 > b > -21
Thus:
b < -17.
Add together a < 4 and b < -17:
a + b < 4 + (-17)
a + b < -13.
Thus, the greatest possible integer value for a+b = -14.
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-13 < 7a + 1 < 29 --> -14 < 7a < 28 --> -2 < a < 4uniyal01 wrote:If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of a + b
So a can be any number less than 4, such as 3.99999999.
19 < 2 - b < 23 --> 17 < -b < 21
When you multiply an inequality by a negative number, reverse the direction of the inequality.
-17 > b > -21
So the maximum value of b is just below -17, something along the lines of -17.000000001.
The question asks for the maximum possible INTEGER value of a + b.
The maximum value of a + b = (3 + some decimal) + (-17 - some decimal) = -14 + some decimal - some decimal.
There is no way the decimals can get a + b to -13. So the answer is -14.
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