5x+2>= 8x-4

{ "query": { "display": "$$5x+2\\ge\\:8x-4$$", "symbolab_question": "EQUATION#5x+2\\ge 8x-4" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Inequalities", "subTopic": "Linear", "default": "x\\le 2", "interval": "(-\\infty ,2]", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$5x+2\\ge\\:8x-4{\\quad:\\quad}x\\le\\:2$$", "input": "5x+2\\ge\\:8x-4", "steps": [ { "type": "interim", "title": "Move $$2\\:$$to the right side", "input": "5x+2\\ge\\:8x-4", "result": "5x\\ge\\:8x-6", "steps": [ { "type": "step", "primary": "Subtract $$2$$ from both sides", "result": "5x+2-2\\ge\\:8x-4-2" }, { "type": "step", "primary": "Simplify", "result": "5x\\ge\\:8x-6" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Move $$8x\\:$$to the left side", "input": "5x\\ge\\:8x-6", "result": "-3x\\ge\\:-6", "steps": [ { "type": "step", "primary": "Subtract $$8x$$ from both sides", "result": "5x-8x\\ge\\:8x-6-8x" }, { "type": "step", "primary": "Simplify", "result": "-3x\\ge\\:-6" } ], "meta": { "interimType": "Move to the Left Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Multiply both sides by $$-1$$", "input": "-3x\\ge\\:-6", "result": "3x\\le\\:6", "steps": [ { "type": "step", "primary": "Multiply both sides by -1 (reverse the inequality)", "result": "\\left(-3x\\right)\\left(-1\\right)\\le\\:\\left(-6\\right)\\left(-1\\right)" }, { "type": "step", "primary": "Simplify", "result": "3x\\le\\:6" } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$3$$", "input": "3x\\le\\:6", "result": "x\\le\\:2", "steps": [ { "type": "step", "primary": "Divide both sides by $$3$$", "result": "\\frac{3x}{3}\\le\\:\\frac{6}{3}" }, { "type": "step", "primary": "Simplify", "result": "x\\le\\:2" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": 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