8 Four distinct positive integers are \(( 3 x - 5 ) , ( 2 x + 3 ) , ( x + 1 )\) and \(( 4 x - 13 )\).
- Explain why \(x \geqslant 4\).
- The four integers are to be sorted into ascending order using a bubble sort.
The original list is
\(\begin{array} { c c c c } ( 3 x - 5 ) & ( 2 x + 3 ) & ( x + 1 ) & ( 4 x - 13 ) \end{array}\)
After the first pass, the list is
\(( 3 x - 5 ) \quad ( x + 1 ) \quad ( 4 x - 13 ) \quad ( 2 x + 3 )\)
After the second pass, the list is
\(( x + 1 )\)
\(( 4 x - 13 )\)
\(( 3 x - 5 )\)
\(( 2 x + 3 )\)
After the third pass, the list is
\(( 4 x - 13 ) \quad ( x + 1 )\)
\(( 3 x - 5 )\)
( \(2 x + 3\) )
- By considering the list after the first pass, write down three inequalities in terms of \(x\).
- By considering the list after the second pass, write down two further inequalities in terms of \(x\).
- By considering the list after the third pass, write down one further inequality in terms of \(x\).
- Hence, by considering the results above, find the value of \(x\).
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