-40b8-8031-f2fe3bb38e46","slug":"find-the-range-of-x-for-the-inequality-sqrtx2-16-3-k31aq","difficulty":"medium","question_text":"Find the range of $x$ for the inequality $\\sqrt{x^2 - 16} < 3$.","choices":[{"id":"a","text":"$$4 < x < 5$"},{"id":"b","text":"$$-5 < x \\leq -4$ or $4 \\leq x < 5$"},{"id":"c","text":"$$x > 5$"},{"id":"d","text":"$$-5 < x < 5$"}],"correct_ids":["b"],"solution":"**Step 1:** Domain requires $x^2 - 16 \\geq 0 \\Rightarrow |x| \\geq 4$. \n**Step 2:** Square both sides: $x^2 - 16 < 9 \\Rightarrow x^2 < 25 \\Rightarrow |x| < 5$. \n**Step 3:** Combine: $4 \\leq |x| < 5$.","created_at":"2026-06-07T01:38:30.518284+00:00","updated_at":"2026-10-14T04:38:57.023293+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"}],["$","title","2",{"children":"Ononot — Find the range of x for the inequality \\sqrt{x^2 - 16} < 3."}],["$","meta","3",{"name":"description","content":"Find the range of x for the inequality \\sqrt{x^2 - 16} < 3."}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","link","5",{"rel":"canonical","href":"https://ononot.com/questions/find-the-range-of-x-for-the-inequality-sqrtx2-16-3-k31aq"}],["$","meta","6",{"property":"og:title","content":"Ononot — Find the range of x for the inequality \\sqrt{x^2 - 16} < 3."}],["$","meta","7",{"property":"og:description","content":"Find the range of x for the inequality \\sqrt{x^2 - 16} < 3."}],["$","meta","8",{"property":"og:url","content":"https://ononot.com/questions/find-the-range-of-x-for-the-inequality-sqrtx2-16-3-k31aq"}],["$","meta","9",{"property":"og:type","content":"website"}],["$","meta","10",{"name":"twitter:card","content":"summary"}],["$","meta","11",{"name":"twitter:title","

Find the range of xxx for the inequality x2−16<3\sqrt{x^2 - 16} < 3x2−16​<3.

Find the range of $x$ for the inequality $\sqrt{x^2 - 16} < 3$ .