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It is given in the question that,

A 18 inch string is cut into two where the second piece is 3 inches longer than twice the first.

Let the length of the first piece be x inch.

So length of second piece is

[tex](2x+3)inch[/tex]

And total length is 18 inch. That is

[tex]x+2x+3 =18 \\ 3x+3 = 18 \\ 3x = 15 \\ x =5[/tex]

So the length of the first piece is 5 inch and the length of second piece is

[tex](2*5 +3) = 13 inches[/tex]

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