dransa wrote:
Bunuel wrote:
SOLUTION
If y=|x+5|-|x-5|, then y can take how many integer values?
A. 5
B. 10
C. 11
D. 20
E. 21
Whenx\leq{-5} , then|x+5|=-(x+5)=-x-5 and|x-5|=-(x-5)=5-x .
Hence in this casey=|x+5|-|x-5|=-x-5-(5-x)=-10 .
1 integer value ofy for this range.
When-5<x<5 , then|x+5|=x+5 and|x-5|=-(x-5)=5-x .
Hence in this casey=|x+5|-|x-5|=x+5-(5-x)=2x .
Therefore for this range -10<(y=2x)<10.
19 integer values of y for this range (from -9 to 9, inclusive).
If y=|x+5|-|x-5|, then y can take how many integer values?
A. 5
B. 10
C. 11
D. 20
E. 21
Whenx\leq{-5} , then|x+5|=-(x+5)=-x-5 and|x-5|=-(x-5)=5-x .
Hence in this casey=|x+5|-|x-5|=-x-5-(5-x)=-10 .
1 integer value ofy for this range.
When-5<x<5 , then|x+5|=x+5 and|x-5|=-(x-5)=5-x .
Hence in this casey=|x+5|-|x-5|=x+5-(5-x)=2x .
Therefore for this range -10<(y=2x)<10.
19 integer values of y for this range (from -9 to 9, inclusive).
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