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Tentukan nilai  dari setiap pertidaksamaan berikut...

Tentukan nilai a dari setiap pertidaksamaan berikut ini.

c.  fraction numerator x plus 2 over denominator 3 end fraction minus fraction numerator 2 x plus a over denominator 2 end fraction plus 2 greater or equal than 0 agar mempunyai penyelesaian x less or equal than 25 over 4.

Jawaban:

c.  Diketahui pertidaksamaan fraction numerator x plus 2 over denominator 3 end fraction minus fraction numerator 2 x plus a over denominator 2 end fraction plus 2 greater or equal than 0, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x plus 2 over denominator 3 end fraction minus fraction numerator 2 x plus a over denominator 2 end fraction plus 2 end cell greater or equal than 0 row cell fraction numerator 2 open parentheses x plus 2 close parentheses over denominator 2 times 3 end fraction minus fraction numerator 3 open parentheses 2 x plus a close parentheses over denominator 3 times 2 end fraction plus 12 over 6 end cell greater or equal than 0 row cell fraction numerator 2 open parentheses x plus 2 close parentheses minus 3 open parentheses 2 x plus a close parentheses plus 12 over denominator 6 end fraction end cell greater or equal than 0 row cell open parentheses fraction numerator 2 open parentheses x plus 2 close parentheses minus 3 open parentheses 2 x plus a close parentheses plus 12 over denominator 6 end fraction close parentheses times 6 end cell greater or equal than cell 0 times 6 end cell row cell 2 open parentheses x plus 2 close parentheses minus 3 open parentheses 2 x plus a close parentheses plus 12 end cell greater or equal than 0 row cell 2 x plus 4 minus 6 x minus 3 a plus 12 end cell greater or equal than 0 row cell 2 x minus 6 x plus 4 plus 12 minus 3 a end cell greater or equal than 0 row cell negative 4 x plus 16 minus 3 a end cell greater or equal than 0 row cell negative 4 x plus open parentheses 16 minus 3 a close parentheses minus open parentheses 16 minus 3 a close parentheses end cell greater or equal than cell 0 minus open parentheses 16 minus 3 a close parentheses end cell row cell negative 4 x end cell greater or equal than cell negative 16 plus 3 a end cell row cell negative 4 x times open parentheses negative 1 fourth close parentheses end cell less or equal than cell open parentheses negative 16 plus 3 a close parentheses times open parentheses negative 1 fourth close parentheses end cell row x less or equal than cell open parentheses negative 16 close parentheses times open parentheses negative 1 fourth close parentheses plus 3 a times open parentheses negative 1 fourth close parentheses end cell row x less or equal than cell 4 minus 3 over 4 a end cell end table

Kemudian, pertidaksamaan x less or equal than 4 minus 3 over 4 a agar mempunyai penyelesaian x less or equal than 25 over 4, maka 4 minus 3 over 4 a equals 25 over 4. Nilai a yang memenuhi sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 minus 3 over 4 a end cell equals cell 25 over 4 end cell row cell 16 over 4 minus 3 over 4 a end cell equals cell 25 over 4 end cell row cell fraction numerator 16 minus 3 a over denominator 4 end fraction end cell equals cell 25 over 4 end cell row cell open parentheses fraction numerator 16 minus 3 a over denominator 4 end fraction close parentheses times 4 end cell equals cell 25 over 4 times 4 end cell row cell 16 minus 3 a end cell equals 25 row cell 16 minus 3 a minus 16 end cell equals cell 25 minus 16 end cell row cell negative 3 a end cell equals 9 row cell negative 3 a times open parentheses negative 1 third close parentheses end cell equals cell 9 times open parentheses negative 1 third close parentheses end cell row a equals cell negative 3 end cell end table


Dengan demikian, nilai a yang memenuhi pertidaksamaan  fraction numerator x plus 2 over denominator 3 end fraction minus fraction numerator 2 x plus a over denominator 2 end fraction plus 2 greater or equal than 0 agar mempunyai penyelesaian x less or equal than 25 over 4 adalah a equals negative 3.

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