{ "query": { "display": "$$\\frac{x}{2}\\ge\\:6$$", "symbolab_question": "EQUATION#\\frac{x}{2}\\ge 6" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Inequalities", "subTopic": "Linear", "default": "x\\ge 12", "interval": "[12,\\infty )", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{x}{2}\\ge\\:6{\\quad:\\quad}x\\ge\\:12$$", "input": "\\frac{x}{2}\\ge\\:6", "steps": [ { "type": "interim", "title": "Multiply both sides by $$2$$", "input": "\\frac{x}{2}\\ge\\:6", "result": "x\\ge\\:12", "steps": [ { "type": "step", "primary": "Multiply both sides by $$2$$", "result": "\\frac{2x}{2}\\ge\\:6\\cdot\\:2" }, { "type": "step", "primary": "Simplify", "result": "x\\ge\\:12" } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Inequalities", "practiceLink": "/practice/inequalities-practice#area=main&subtopic=Linear", "practiceTopic": "Linear Inequalities" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "funcsToDraw": { "funcs": [ { "evalFormula": "x=12", "displayFormula": "x=12", "attributes": { "color": "GRAY", "lineType": "BOLD", "isAsymptote": false } } ] }, "fills": [ { "ranges": [ { "fst": "12.0", "snd": "Infinity" } ], "funcIndices": [], "funcs": [], "xIneq": true, "yIneq": false, "twoVar": false, "trueAboveLine": false, "color": "rgba(171, 181, 235, 0.3)" } ], "functionChanges": [ { "origFormulaLatex": [], "finalFormulaLatex": [], "plotTitle": "x\\ge 12", "paramsLatex": [], "paramsReplacementsLatex": [] } ], "localBoundingBox": { "xMin": -2.0571428571428574, "xMax": 14.4, "yMin": -2, "yMax": 8 }, "intervals": [ { "mind": 12, "minInclusive": true, "maxInclusive": false, "maxFinite": false, "minFinite": true, "isAllR": false, "isPoint": false } ], "imageAPI": "x\\ge 12" }, "showViewLarger": true } }, "meta": { "showVerify": true } }