Choosing k so that two inequalities share exactly three integers
Choosing k so that two inequalities share exactly three integers
IP 2
6 marks
The inequalities \(3x-k\le2x+5\) and \(4-x<2x+1\) are to be satisfied simultaneously, where \(k\) is a constant.
- Solve each inequality for \(x\), giving the first in terms of \(k\).[2]
- Given that there are exactly three integers that satisfy both inequalities, find the range of values of \(k\).[4]
Solution:
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Answer:(a) \(x\le k+5\), \(x>1\) (b) \(-1\le k<0\)
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