|9+x|=4

{ "query": { "display": "$$\\left|9+x\\right|=4$$", "symbolab_question": "EQUATION#\\left|9+x\\right|=4" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Equations", "subTopic": "Absolute", "default": "x=-13\\lor x=-5", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\left|9+x\\right|=4{\\quad:\\quad}x=-13\\lor\\:x=-5$$", "input": "\\left|9+x\\right|=4", "steps": [ { "type": "step", "primary": "Apply absolute rule: If $$|u|\\:=\\:a,\\:a>0\\:$$then $$u\\:=\\:a\\:\\quad\\:$$or$$\\quad\\:u\\:=\\:-a$$", "result": "9+x=-4\\lor\\:9+x=4" }, { "type": "interim", "title": "$$9+x=-4\\lor\\:9+x=4$$", "input": "9+x=-4\\lor\\:9+x=4", "result": "x=-13\\lor\\:x=-5", "steps": [ { "type": "interim", "title": "$$9+x=-4{\\quad:\\quad}x=-13$$", "input": "9+x=-4", "steps": [ { "type": "interim", "title": "Move $$9\\:$$to the right side", "input": "9+x=-4", "result": "x=-13", "steps": [ { "type": "step", "primary": "Subtract $$9$$ from both sides", "result": "9+x-9=-4-9" }, { "type": "step", "primary": "Simplify", "result": "x=-13" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Equations" } }, { "type": "interim", "title": "$$9+x=4{\\quad:\\quad}x=-5$$", "input": "9+x=4", "steps": [ { "type": "interim", "title": "Move $$9\\:$$to the right side", "input": "9+x=4", "result": "x=-5", "steps": [ { "type": "step", "primary": "Subtract $$9$$ from both sides", "result": "9+x-9=4-9" }, { "type": "step", "primary": "Simplify", "result": "x=-5" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Equations" } }, { "type": "step", "primary": "Combine Solutions:", "result": "x=-13\\lor\\:x=-5" } ], "meta": { "interimType": "N/A" } } ], "meta": { "solvingClass": "Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\left|9+x\\right|-4" }, "showViewLarger": true } }, "meta": { "showVerify": true } }