Pertanyaan

Tentukan nilai x yang memenuhi pertidaksamaan berikut. e. x − 2 1 − x ≥ x − 4 x − 3

Tentukan nilai $x$ yang memenuhi pertidaksamaan berikut.

e. $\frac{1 - x}{x - 2} \geq \frac{x - 3}{x - 4}$

M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

dapat disimpulkan bahwa nilai yang memenuhi pertidaksamaan adalah .

dapat disimpulkan bahwa nilai

yang memenuhi pertidaksamaan $fraction numerator size 14px 1 size 14px minus size 14px x over denominator size 14px x size 14px minus size 14px 2 end fraction size 14px greater or equal than fraction numerator size 14px x size 14px minus size 14px 3 over denominator size 14px x size 14px minus size 14px 4 end fraction$ adalah $begin mathsize 14px style fraction numerator 5 minus square root of 5 over denominator 2 end fraction less or equal than x less than 2 space atau space fraction numerator 5 plus square root of 5 over denominator 2 end fraction less or equal than x less than 4 end style$ .

Pembahasan

Langkah 1 : Menentukan angka angka batas Langkah 2 : Menentukan syarat lain Langkah 3 : Menentukan daerah arsiran penyelesaian Jadi daerah penyelesaian : Jadi, dapat disimpulkan bahwa nilai yang memenuhi pertidaksamaan adalah .

Langkah 1 : Menentukan angka angka batas

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 minus x over denominator x minus 2 end fraction end cell greater or equal than cell fraction numerator x minus 3 over denominator x minus 4 end fraction end cell row cell fraction numerator 1 minus x over denominator x minus 2 end fraction minus fraction numerator x minus 3 over denominator x minus 4 end fraction end cell greater or equal than 0 row cell fraction numerator open parentheses 1 minus x close parentheses open parentheses x minus 4 close parentheses over denominator open parentheses x minus 2 close parentheses open parentheses x minus 4 close parentheses end fraction minus fraction numerator open parentheses x minus 3 close parentheses open parentheses x minus 2 close parentheses over denominator left parenthesis x minus 2 right parenthesis left parenthesis x minus 4 right parenthesis end fraction end cell greater or equal than 0 row cell fraction numerator x minus 4 minus x squared plus 4 x over denominator left parenthesis x minus 2 right parenthesis left parenthesis x minus 4 right parenthesis end fraction minus fraction numerator x squared minus 5 x plus 6 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x minus 4 right parenthesis end fraction end cell greater or equal than 0 row cell fraction numerator negative 2 x squared plus 10 x minus 10 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x minus 4 right parenthesis end fraction end cell greater or equal than 0 row cell fraction numerator negative left parenthesis 2 x squared minus 10 x plus 10 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x minus 4 right parenthesis end fraction end cell greater or equal than 0 row blank blank cell fraction numerator negative 2 open parentheses x squared minus 5 x plus 5 close parentheses over denominator left parenthesis x minus 2 right parenthesis left parenthesis x minus 4 right parenthesis end fraction end cell row blank blank cell Angka space batas space colon end cell row blank blank cell Faktor space dari space straight x squared minus 5 straight x plus 5 space adalah space colon end cell row cell x subscript 1 comma x subscript 2 end cell equals cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end cell row blank equals cell fraction numerator negative open parentheses negative 5 close parentheses plus-or-minus square root of open parentheses negative 5 close parentheses squared minus 4 open parentheses 1 close parentheses open parentheses 5 close parentheses end root over denominator 2 open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator 5 plus-or-minus square root of 25 minus 20 end root over denominator 2 end fraction end cell row blank equals cell fraction numerator 5 plus-or-minus square root of 5 over denominator 2 end fraction end cell row cell x subscript 1 end cell equals cell fraction numerator 5 plus square root of 5 over denominator 2 end fraction end cell row cell x subscript 2 end cell equals cell fraction numerator 5 minus square root of 5 over denominator 2 end fraction end cell row blank blank blank row blank blank cell Angka space batas space yang space lain colon end cell row cell x minus 2 end cell equals 0 row x equals 2 row blank blank blank row cell x minus 4 end cell equals 0 row x equals 4 row blank blank blank end table end style$

Langkah 2 : Menentukan syarat lain

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 2 end cell not equal to 0 row x not equal to 2 row blank blank blank row cell x minus 4 end cell not equal to 0 row x not equal to 4 end table end style

Langkah 3 : Menentukan daerah arsiran penyelesaian

Jadi daerah penyelesaian :

$begin mathsize 14px style fraction numerator 5 minus square root of 5 over denominator 2 end fraction less or equal than x less than 2 space atau space fraction numerator 5 plus square root of 5 over denominator 2 end fraction less or equal than x less than 4 end style$

Jadi, dapat disimpulkan bahwa nilai yang memenuhi pertidaksamaan $fraction numerator size 14px 1 size 14px minus size 14px x over denominator size 14px x size 14px minus size 14px 2 end fraction size 14px greater or equal than fraction numerator size 14px x size 14px minus size 14px 3 over denominator size 14px x size 14px minus size 14px 4 end fraction$ adalah $begin mathsize 14px style fraction numerator 5 minus square root of 5 over denominator 2 end fraction less or equal than x less than 2 space atau space fraction numerator 5 plus square root of 5 over denominator 2 end fraction less or equal than x less than 4 end style$ .