x/8+x/4 =-1

{ "query": { "display": "$$\\frac{x}{8}+\\frac{x}{4}=-1$$", "symbolab_question": "EQUATION#\\frac{x}{8}+\\frac{x}{4}=-1" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Equations", "subTopic": "Linear", "default": "x=-\\frac{8}{3}", "decimal": "x=-2.66666…", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{x}{8}+\\frac{x}{4}=-1{\\quad:\\quad}x=-\\frac{8}{3}$$", "input": "\\frac{x}{8}+\\frac{x}{4}=-1", "steps": [ { "type": "interim", "title": "Multiply by LCM", "input": "\\frac{x}{8}+\\frac{x}{4}=-1", "result": "3x=-8", "steps": [ { "type": "interim", "title": "Find Least Common Multiplier of $$8,\\:4:{\\quad}8$$", "input": "8,\\:4", "steps": [ { "type": "definition", "title": "Least Common Multiplier (LCM)", "text": "The LCM of $$a,\\:b$$ is the smallest positive number that is divisible by both $$a$$ and $$b$$" }, { "type": "interim", "title": "Prime factorization of $$8:{\\quad}2\\cdot\\:2\\cdot\\:2$$", "input": "8", "steps": [ { "type": "step", "primary": "$$8\\:$$divides by $$2\\quad\\:8=4\\cdot\\:2$$", "result": "=2\\cdot\\:4" }, { "type": "step", "primary": "$$4\\:$$divides by $$2\\quad\\:4=2\\cdot\\:2$$", "result": "=2\\cdot\\:2\\cdot\\:2" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRtXnBik8vDPXVw+nKWp28DI/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp1RcgsS082tQWmOBW6FvhEw" } }, { "type": "interim", "title": "Prime factorization of $$4:{\\quad}2\\cdot\\:2$$", "input": "4", "steps": [ { "type": "step", "primary": "$$4\\:$$divides by $$2\\quad\\:4=2\\cdot\\:2$$", "result": "=2\\cdot\\:2" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRsG/uC0ndYtZpJL4uAxK7FI/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp39fF/zAtU5baHQ1hwgXA+n" } }, { "type": "step", "primary": "Multiply each factor the greatest number of times it occurs in either $$8$$ or $$4$$", "result": "=2\\cdot\\:2\\cdot\\:2" }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:2\\cdot\\:2=8$$", "result": "=8" } ], "meta": { "solvingClass": "LCM", "interimType": "LCM Top in Equation Title 1Eq" } }, { "type": "step", "primary": "Multiply by LCM=$$8$$", "result": "\\frac{x}{8}\\cdot\\:8+\\frac{x}{4}\\cdot\\:8=-1\\cdot\\:8" }, { "type": "interim", "title": "Simplify", "input": "\\frac{x}{8}\\cdot\\:8+\\frac{x}{4}\\cdot\\:8=-1\\cdot\\:8", "result": "3x=-8", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{x}{8}\\cdot\\:8:{\\quad}x$$", "input": "\\frac{x}{8}\\cdot\\:8", "steps": [ { "type": "step", "primary": "Multiply fractions: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$", "result": "=\\frac{x\\cdot\\:8}{8}" }, { "type": "step", "primary": "Cancel the common factor: $$8$$", "result": "=x" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7fAu76bLsHyzNciUVCyBLF/OQKlvRvVM0xRaof3zDNGarju+5Z51e/ZZSD3gRHwjBvZTuV3pU1o5URU/sdf9xYZjcBIL5pmo83UMFZRSzJsWQA7yHY4blmznYtOPht2hnzf67KGe0cAgTBx8mejyCUQ==" } }, { "type": "interim", "title": "Simplify $$\\frac{x}{4}\\cdot\\:8:{\\quad}2x$$", "input": "\\frac{x}{4}\\cdot\\:8", "steps": [ { "type": "step", "primary": "Multiply fractions: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$", "result": "=\\frac{x\\cdot\\:8}{4}" }, { "type": "step", "primary": "Divide the numbers: $$\\frac{8}{4}=2$$", "result": "=2x" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7HujeYqtVS6bD5mqN7Rg2Y/OQKlvRvVM0xRaof3zDNGarju+5Z51e/ZZSD3gRHwjBgdPTKtotjHTYDQdAKjyGMosaY2cs9YZ/08feWmaOgkj7GTdsBoChJvoAZssbF+dqbASzXfkfbqfgm9dDZ7pWcQ==" } }, { "type": "interim", "title": "Simplify $$-1\\cdot\\:8:{\\quad}-8$$", "input": "-1\\cdot\\:8", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$1\\cdot\\:8=8$$", "result": "=-8" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7+clio325OVjNlTIdpl8GRiAn9lkDfZkicUGkO3EF+IqLaeGhfPxl9m3N3atI3revgQUxJPyUNnGfVirkcwpVO+dzqilyMdAftDhxIDf7Leg9nMtMD1D++j34aX4IVCU5" } }, { "type": "step", "result": "x+2x=-8" }, { "type": "step", "result": "3x=-8" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Equation LCM Multiply Title 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjAjYcBSbJJKcO5nwp2W+NzB6O4Hdd6+pVFvXhuRP58ioaUJTXRIJ+xuJHtw/VpW7zN2BQR0dJUGN2TRuXDsmO1Xq2/AmneVbzs8wajHeHzZ60UqTd96MWTKI6Kr2Ib0iQDpjtzABgWAdI9SH55k29/dkDtt6Z9KIv/y3s8wrVBpKg==" } }, { "type": "interim", "title": "Divide both sides by $$3$$", "input": "3x=-8", "result": "x=-\\frac{8}{3}", "steps": [ { "type": "step", "primary": "Divide both sides by $$3$$", "result": "\\frac{3x}{3}=\\frac{-8}{3}" }, { "type": "step", "primary": "Simplify", "result": "x=-\\frac{8}{3}" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7TRwQSStqkHRxeIzqgPTpwpN1pXT08zEQpn0WJ6CFMXBgNJ67EOD8lvNAD3ifVxEoJI4KD5IMC4UmvgwFppsKgo3o0MiPQMvyHAXtG9ax95IA1vSE7Gc8ILn/oj5ZNzzUz27xpiicCLlej+r3Kqpg6rOnDLD0jssdVCDGYRPtoVT3rULl/hDWwC6b+Lvj4auBkl2nMYoMvCLXtVESz9/y9wwKAu7Z3tN/RgLPjlzyRw8i5OoNNprqQV2UgQUGESqFlvjhqQs5XJJkHv2GQUE6glcrAOsROfiVgP+wtWyh0afthvwKEoR3ksHNHbCkrb6kcwDIfxbr/Pq2vWjsXBdpmP+Gc7uNDn5rFMiDyv69niKC8VZfRwvJI6wrKTATUX8dU9cwwVwt4DorvBqyqIystksCgBQLPiLZrslDBUCYri8=" } } ], "meta": { "solvingClass": "Equations", "practiceLink": "/practice/linear-equations-practice", "practiceTopic": "Linear Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\frac{x}{8}+\\frac{x}{4}=-1" }, "showViewLarger": true } }, "meta": { "showVerify": true } }