ext":"Solve $\\frac{|x|-3}{|x|+2} < 0$.","choices":[{"id":"a","text":"(-3, 3)"},{"id":"b","text":"(-2, 2)"},{"id":"c","text":"(-3, 3) \\setminus \\{0\\}"},{"id":"d","text":"(-\\infty, -3) \\cup (3, \\infty)"}],"correct_ids":["a"],"solution":"Since $|x|+2$ is always positive, the inequality is equivalent to $|x|-3 < 0$, which is $|x| < 3$, or $-3 < x < 3$.","created_at":"2026-06-13T17:26:45.04186+00:00","updated_at":"2026-06-13T17:26:45.04186+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"}],["$","title","2",{"children":"Ononot — Solve \\frac{|x|-3}{|x|+2} < 0."}],["$","meta","3",{"name":"description","content":"Solve \\frac{|x|-3}{|x|+2} < 0."}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","link","5",{"rel":"canonical","href":"https://ononot.com/questions/solve-fracx-3x2-0-6vpm6"}],["$","meta","6",{"property":"og:title","content":"Ononot — Solve \\frac{|x|-3}{|x|+2} < 0."}],["$","meta","7",{"property":"og:description","content":"Solve \\frac{|x|-3}{|x|+2} < 0."}],["$","meta","8",{"property":"og:url","content":"https://ononot.com/questions/solve-fracx-3x2-0-6vpm6"}],["$","meta","9",{"property":"og:type","content":"website"}],["$","meta","10",{"name":"twitter:card","content":"summary"}],["$","meta","11",{"name":"twitter:title","content":"Ononot — Solve \\frac{|x|-3}{|x|+2} < 0."}],["$","meta","12",{"name":"twitter:description","content":"Solve \\frac{|x|-3}{|x|+2} < 0."}],["$","link","13",{"rel":"icon","href":"/favicon.ico","type":"image/x-icon","sizes":"16x16"}]] 4:null

Solve ∣x∣−3∣x∣+2<0\frac{|x|-3}{|x|+2} < 0∣x∣+2∣x∣−3​<0.

Solve $\frac{|x|-3}{|x|+2} < 0$ .