{ "query": { "display": "$$25\\cdot\\:42-25\\cdot\\:2x=348$$", "symbolab_question": "EQUATION#25\\cdot 42-25\\cdot 2x=348" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Equations", "subTopic": "Linear", "default": "x=\\frac{351}{25}", "decimal": "x=14.04", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$25\\cdot\\:42-25\\cdot\\:2x=348{\\quad:\\quad}x=\\frac{351}{25}$$", "input": "25\\cdot\\:42-25\\cdot\\:2x=348", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$25\\cdot\\:42=1050$$", "result": "1050-25\\cdot\\:2x=348" }, { "type": "step", "primary": "Multiply the numbers: $$25\\cdot\\:2=50$$", "result": "1050-50x=348" }, { "type": "interim", "title": "Move $$1050\\:$$to the right side", "input": "1050-50x=348", "result": "-50x=-702", "steps": [ { "type": "step", "primary": "Subtract $$1050$$ from both sides", "result": "1050-50x-1050=348-1050" }, { "type": "step", "primary": "Simplify", "result": "-50x=-702" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s71IDEP4b8ERLbIjt3JxF7r5Nerv1uh1f69MMd82JJQGXNKtCo/Zfa6g+7HBHjW9VdkB93oYIvdzv+qAAizA6SMYCqiacXnRmza3yMD5APjuVn1t4F3di//58KWDoruHXRiS267MvT1JLdT5GyDEcYVcz8sCqFW4KRMi5zptad+UisoAiCZLxb22KZVtGIU1iNS3D4Die0wB8SlCsv2r53JRWTy3ZPCOH7OOn12VhNyj8aDBJshx3kmM/93Uq4Jtb3jMNJ/a+H+L7ezhw7+grBnLWsrD7vZXjUuDF4I55wpc58i+1EUi0JR87vYNuUkO+vpqDfn2ckgJI3FHWx2SIlgPC30sSftAIFS6Qkpy19IkrR+tiFZ0LpaWQERgZ6emkvnKnhTb5FuLvnspCukKVm1G6oAniakxKtba7b+vFRQes=" } }, { "type": "interim", "title": "Divide both sides by $$-50$$", "input": "-50x=-702", "result": "x=\\frac{351}{25}", "steps": [ { "type": "step", "primary": "Divide both sides by $$-50$$", "result": "\\frac{-50x}{-50}=\\frac{-702}{-50}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{-50x}{-50}=\\frac{-702}{-50}", "result": "x=\\frac{351}{25}", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{-50x}{-50}:{\\quad}x$$", "input": "\\frac{-50x}{-50}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{-a}{-b}=\\frac{a}{b}$$", "result": "=\\frac{50x}{50}" }, { "type": "step", "primary": "Divide the numbers: $$\\frac{50}{50}=1$$", "result": "=x" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7IPUJGuqfHB+Pf9oXm4hcggGP3HWx2+i/1VX7HMYZTqyjkVi15I8rBefLi4Iyt2wrNnlcfYSxPIgsp1FH5TTQYHKF3u2OIb4bFA3EO8aRlSUwEYx2ejqZubzAeb43X2m86ng0ANBBnlpM7FKs67ynvQ==" } }, { "type": "interim", "title": "Simplify $$\\frac{-702}{-50}:{\\quad}\\frac{351}{25}$$", "input": "\\frac{-702}{-50}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{-a}{-b}=\\frac{a}{b}$$", "result": "=\\frac{702}{50}" }, { "type": "step", "primary": "Cancel the common factor: $$2$$", "result": "=\\frac{351}{25}" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7+QsOrvvQWTyuPvqPkGyKLQGP3HWx2+i/1VX7HMYZTqyjkVi15I8rBefLi4Iyt2wrcrF4TMjH1ZWQQl1zhhox32RLd2VwIqlBNByF6663syR2SpdpleAJc7YgKUwBYoM96QgY/JijCdxOjHvTMbAiYeyaUU+keuRe0k1/Vt5lwW4=" } }, { "type": "step", "result": "x=\\frac{351}{25}" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "practiceLink": "/practice/linear-equations-practice", "practiceTopic": "Linear Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "25\\cdot 42-25\\cdot 2x=348" }, "showViewLarger": true } }, "meta": { "showVerify": true } }