aa-b627-423b-b47c-2702ba8b2758","topic_id":"94ea51ee-c689-4e0e-9acf-7d6754bf0285","slug":"determine-the-set-of-values-for-x-such-that-fracx2-7x-10x-2-mibs2","difficulty":"hard","question_text":"Determine the set of values for $x$ such that $\\frac{x^2 - 7x + 10}{x - 2} < 0$.","choices":[{"id":"a","text":"$$x < 5, x \\neq 2$"},{"id":"b","text":"$$x < 2$"},{"id":"c","text":"$$2 < x < 5$"},{"id":"d","text":"$$x > 5$"}],"correct_ids":["a"],"solution":"Simplify $\\frac{(x-5)(x-2)}{x-2} < 0$. For $x \\neq 2$, this simplifies to $x-5 < 0$, which is $x < 5$. Since $x$ cannot be 2, the domain is $x < 5$ and $x \\neq 2$.","created_at":"2026-06-13T17:41:32.78245+00:00","updated_at":"2026-06-13T17:41:32.78245+00:00","diagram_svg":null,"human_approved":false,"user_approved":false,"ai_approved":false,"ai_review":null,"topic":{"name":"Rational Expressions","slug":"algebra_rational_expressions","description":"Simplifying, solving rational equations"}},"user":null,"initialGuestCount":0}]}]]}] f:[["$","meta","0",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["$","meta","1",{"charSet":"utf-8"}],["$","title","2",{"children":"Ononot — Determine the set of values for x such that \\frac{x^2 - 7x +"}],["$","meta","3",{"name":"description","content":"Determine the set of values for x such that \\frac{x^2 - 7x + 10}{x - 2} < 0."}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","link","5",{"rel":"canonical","href":"https://ononot.com/questions/determine-the-set-of-values-for-x-such-that-fracx2-7x-10x-2-mibs2"}],["$","meta","6",{"property":"og:title","content":"Ononot — Determine the set of values for x such that \\frac{x^2 - 7x +"}],["$","meta","7",{"property":"og:description","content":"Determine the set of values for x such that \\frac{x^2 - 7x + 10}{x - 2} < 0."}],["$","meta","8",{"property":"og:url","content":"https://ononot.com/questions/determine-the-set-of-values-for-x-such-that-fracx2-7x-10x-2-mibs2"}],["$","meta","9",{"property":"og:type","content":"website"}],["$","meta","10",{"name":

Determine the set of values for xxx such that x2−7x+10x−2<0\frac{x^2 - 7x + 10}{x - 2} < 0x−2x2−7x+10​<0.

Determine the set of values for $x$ such that $\frac{x^2 - 7x + 10}{x - 2} < 0$ .