| n/4 |<= 3\mid

{ "query": { "display": "$$\\left|\\frac{n}{4}\\right|\\le\\:3\\mid$$", "symbolab_question": "EQUATION#\\left|\\frac{n}{4}\\right|\\le 3\\mid " }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Inequalities", "subTopic": "Absolute", "default": "\\mathrm{No\\:Solution}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\left|\\frac{n}{4}\\right|\\le\\:3\\mid\\:{\\quad:\\quad}$$No Solution", "input": "\\left|\\frac{n}{4}\\right|\\le\\:3\\mid\\:", "steps": [ { "type": "step", "primary": "Apply absolute rule: If $$|u|\\:\\leq\\:a,\\:a\\:>\\:0\\:$$then $$-a\\:\\leq\\:u\\:\\leq\\:a$$", "result": "-3\\left|\\le\\:\\frac{n}{4}\\le\\:3\\right|" }, { "type": "interim", "title": "$$\\frac{n}{4}\\ge\\:-3\\left|\\land\\:\\frac{n}{4}\\le\\:3\\right|$$", "input": "\\frac{n}{4}\\ge\\:-3\\left|\\land\\:\\frac{n}{4}\\le\\:3\\right|", "result": "\\mathrm{No\\:Solution}\\land\\:\\mathrm{No\\:Solution}", "steps": [ { "type": "interim", "title": "$$\\frac{n}{4}\\ge\\:-3\\mid\\:{\\quad:\\quad}n\\ge\\:-12\\mid\\:$$", "input": "\\frac{n}{4}\\ge\\:-3\\mid\\:", "steps": [ { "type": "interim", "title": "Multiply both sides by $$4$$", "input": "\\frac{n}{4}\\ge\\:-3\\mid\\:", "result": "n\\ge\\:-12\\mid\\:", "steps": [ { "type": "step", "primary": "Multiply both sides by $$4$$", "result": "\\frac{4n}{4}\\ge\\:4\\left(-3\\mid\\:\\right)" }, { "type": "step", "primary": "Simplify", "result": "n\\ge\\:-12\\mid\\:" } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYjUN23ZVK89227jwmt37fZcVOZiYrkka/WOeQU+IV8eqZXoejBGTAlgxfQZNyTWDMWp3wfSyITtsqOKGZTLs+WDLAFWGeKhPsKR9oNoiDBvH2UHZ9PEnUJcU2+GDBiohTYktuuzL09SS3U+RsgxHGFXM/LAqhVuCkTIuc6bWnflI6Yr8k1ZjvkZ+UcEKRTBQ+5gxksqIOerSDrT0wR2B+gIyA64P4UVqUSlW1+Gn+ty4hahQUY/2AVdtRZ1sXkomRrXVtBClpOReHN/jED3U6Zdx/bmVxxZmRyGu3FS+8KhLS3D4Die0wB8SlCsv2r53JRWTy3ZPCOH7OOn12VhNyj8aDBJshx3kmM/93Uq4Jtb3jMNJ/a+H+L7ezhw7+grBnLWsrD7vZXjUuDF4I55wpc58i+1EUi0JR87vYNuUkO+vpqDfn2ckgJI3FHWx2SIlgPC30sSftAIFS6Qkpy19IkpeCrSDQrH/2qU31tb5DJppqOctuj+nzPVlLoqW9SK74Q==" } } ], "meta": { "solvingClass": "Inequalities", "interimType": "Inequalities" } }, { "type": "interim", "title": "$$\\frac{n}{4}\\le\\:3\\mid\\:{\\quad:\\quad}n\\le\\:12\\mid\\:$$", "input": "\\frac{n}{4}\\le\\:3\\mid\\:", "steps": [ { "type": "interim", "title": "Multiply both sides by $$4$$", "input": "\\frac{n}{4}\\le\\:3\\mid\\:", "result": "n\\le\\:12\\mid\\:", "steps": [ { "type": "step", "primary": "Multiply both sides by $$4$$", "result": "\\frac{4n}{4}\\le\\:4\\cdot\\:3\\mid\\:" }, { "type": "step", "primary": "Simplify", "result": "n\\le\\:12\\mid\\:" } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Inequalities", "interimType": "Inequalities" } }, { "type": "step", "primary": "Combine the intervals", "result": "\\mathrm{No\\:Solution}\\land\\:\\mathrm{No\\:Solution}" } ], "meta": { "interimType": "N/A" } }, { "type": "step", "result": "\\mathrm{No\\:Solution\\:for}\\:n\\in\\mathbb{R}" } ], "meta": { "solvingClass": "Inequalities" } }, "meta": { "showVerify": true } }