t":"Solve $\\sqrt{x^2 - 1} < 2 - x$.","choices":[{"id":"a","text":"$$x \\leq -1$"},{"id":"b","text":"$$x \\leq 1.25$"},{"id":"c","text":"$$1 \\leq x < 1.25$"},{"id":"d","text":"$$x \\leq -1$ or $1 \\leq x < 1.25$"}],"correct_ids":["c"],"solution":"Domain: $x^2 - 1 \\geq 0 \\implies x \\in (-\\infty, -1] \\cup [1, \\infty)$. $2-x > 0 \\implies x < 2$. Square: $x^2 - 1 < 4 - 4x + x^2 \\implies 4x < 5 \\implies x < 1.25$. Intersection with domain: $x \\in [1, 1.25)$. Note: $x \\in (-\\infty, -1]$ also satisfies $x^2-1 < (2-x)^2$ because $4x < 5$ is true, but check original: $\\sqrt{\\text{pos}} < \\text{negative}$ is impossible. So $x \\geq 1$ is required.","created_at":"2026-06-13T17:28:03.151016+00:00","updated_at":"2026-06-13T17:28:03.151016+00:00","diagram_svg":null,"human_approved":false,"user_approved":false,"ai_approved":false,"ai_review":null,"topic":{"name":"Inequalities","slug":"algebra_inequalities","description":"Linear, quadratic, absolute value inequalities"}},"user":null,"initialGuestCount":0}]}]]}] f:[["$","meta","0",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["$","meta","1",{"charSet":"utf-8"}],["$","title","2",{"children":"Ononot — Solve \\sqrt{x^2 - 1} < 2 - x."}],["$","meta","3",{"name":"description","content":"Solve \\sqrt{x^2 - 1} < 2 - x."}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","link","5",{"rel":"canonical","href":"https://ononot.com/questions/solve-sqrtx2-1-2-x-24ry1"}],["$","meta","6",{"property":"og:title","content":"Ononot — Solve \\sqrt{x^2 - 1} < 2 - x."}],["$","meta","7",{"property":"og:description","content":"Solve \\sqrt{x^2 - 1} < 2 - x."}],["$","meta","8",{"property":"og:url","content":"https://ononot.com/questions/solve-sqrtx2-1-2-x-24ry1"}],["$","meta","9",{"property":"og:type","content":"website"}],["$","meta","10",{"name":"twitter:card","content":"summary"}],["$","meta","11",{"name":"twitter:title","content":"Ononot — Solve \\sqrt{x^2 - 1} < 2 - x."}],["$","meta","12",{"name":"twitter:description","content":"Solve \\sq

Solve x2−1<2−x\sqrt{x^2 - 1} < 2 - xx2−1​<2−x.

Solve $\sqrt{x^2 - 1} < 2 - x$ .