{"id":"informator-maturalny-matematyka-2010/zad/51","paper_id":"informator-maturalny-matematyka-2010","number":"51","points":2,"ptype":"open","subject":"matematyka","category":"informator-maturalny","year":2010,"month":null,"level":null,"text":"Zadanie 51. (2 pkt)\nRozwiąż równanie 2\n3\n1\n1 2\n2\nx\nx","answer":null,"answer_text":null,"solution":"(2-3x)/(1-2x) = -1/2, dziedzina x≠1/2. Mnożymy na krzyż: 2(2-3x) = -1(1-2x) → 4-6x = -1+2x → 5=8x → x=5/8 (spełnia dziedzinę).\nOdpowiedź: x=5/8.","image":"img/informator-maturalny-matematyka-2010/zad-51.webp","solution_image":null,"topics":null,"page_from":84,"source":"ai","answer_source":null,"answer_text_source":null,"solution_source":"ai","text_source":"ocr","source_label":"Matematyka · Informator maturalny · 2010","subject_label":"Matematyka","category_label":"Informator maturalny","text_html":"<p>Zadanie 51. (2 pkt)<br>Rozwiąż równanie 2<br>3<br>1<br>1 2<br>2<br>x<br>x</p>","solutions":[{"source":"ai","label":"AI","kind":"text","html":"<p>(2-3x)/(1-2x) = -1/2, dziedzina x≠1/2. Mnożymy na krzyż: 2(2-3x) = -1(1-2x) → 4-6x = -1+2x → 5=8x → x=5/8 (spełnia dziedzinę).<br>Odpowiedź: x=5/8.</p>"}]}