Răspuns :
[tex] \frac{12}{17} - x = \frac{15}{34} [/tex]
[tex] - x = \frac{15}{34} - \frac{12}{17} [/tex]
[tex] - x = - \frac{9}{34} [/tex]
[tex]x = \frac{9}{34} [/tex]
[tex] \frac{5}{12} + x + \frac{19}{60} = \frac{26}{15} [/tex]
[tex] \frac{11}{15} + x = \frac{26}{15} [/tex]
[tex]x = \frac{26}{15} - \frac{11}{15} [/tex]
[tex]x = \frac{15}{15} = 1[/tex]
[tex] \frac{7}{4} - x = \frac{7}{8} [/tex]
[tex] - x = \frac{7}{8} - \frac{7}{4} [/tex]
[tex] - x = - \frac{7}{8} [/tex]
[tex]x = \frac{7}{8} [/tex]
[tex] \frac{11}{5} - x = \frac{3}{20} [/tex]
[tex] - x = \frac{3}{20} - \frac{11}{5} [/tex]
[tex] - x = - \frac{41}{20} [/tex]
[tex]x = \frac{41}{20} [/tex]
[tex] \frac{1}{6} - x = \frac{1}{42} [/tex]
[tex] - x = \frac{1}{12} - \frac{1}{6}[/tex]
[tex] -x = - \frac{1}{12} [/tex]
[tex]x = \frac{1}{12} [/tex]
Succes in continuare:))
[tex] - x = \frac{15}{34} - \frac{12}{17} [/tex]
[tex] - x = - \frac{9}{34} [/tex]
[tex]x = \frac{9}{34} [/tex]
[tex] \frac{5}{12} + x + \frac{19}{60} = \frac{26}{15} [/tex]
[tex] \frac{11}{15} + x = \frac{26}{15} [/tex]
[tex]x = \frac{26}{15} - \frac{11}{15} [/tex]
[tex]x = \frac{15}{15} = 1[/tex]
[tex] \frac{7}{4} - x = \frac{7}{8} [/tex]
[tex] - x = \frac{7}{8} - \frac{7}{4} [/tex]
[tex] - x = - \frac{7}{8} [/tex]
[tex]x = \frac{7}{8} [/tex]
[tex] \frac{11}{5} - x = \frac{3}{20} [/tex]
[tex] - x = \frac{3}{20} - \frac{11}{5} [/tex]
[tex] - x = - \frac{41}{20} [/tex]
[tex]x = \frac{41}{20} [/tex]
[tex] \frac{1}{6} - x = \frac{1}{42} [/tex]
[tex] - x = \frac{1}{12} - \frac{1}{6}[/tex]
[tex] -x = - \frac{1}{12} [/tex]
[tex]x = \frac{1}{12} [/tex]
Succes in continuare:))
[tex]a) \frac{12}{17} - x = \frac{15}{34} \\ \\ \frac{ {2}^{2} \times 3 }{17} - x = \frac{15}{34} \\ \\ \frac{ {(2}^{2} \times 3) - 17x }{17} - x = \frac{15}{34} \\ \\ \frac{(4 \times 3) - 17x}{17} = \frac{15}{34} \\ \\ \frac{12 - 17x}{17} = \frac{15}{34} \\ \\ \frac{ - 17x + 12}{17} = \frac{15}{34} \\ \\ \frac{ - 17x + 12}{17} = \frac{15}{2 \times 17} \\ \\ 2( - 17x + 12) = 15 \\ \\ - 2 \times 17x + 2 \times 12 = 15 \\ \\ - 34x + 24 = 15 \\ \\ ( - 34x + 24) + ( - 24) = 15 + ( - 24) \\ \\ - 34x + 24 - 24 = 15 - 24 \\ \\ - 34x = - 9 \\ \\ \frac{34x}{34} = \frac{9}{34} \\ \\ x = \frac{9}{34} [/tex]
[tex]b) \frac{5}{12} + x + \frac{19}{60} = \frac{26}{15} \\ \\ \frac{5}{ {2}^{2} \times 3 } + x + \frac{19}{ {2}^{2} \times 3 \times 5} = \frac{26}{15} \\ \\ \frac{5 \times 5 + ( {2}^{2} \times 3 \times 5)x + 19 }{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{25 + (4 \times 3 \times 5)x + 19}{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{25 + 60x + 19}{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{60x + 25 + 19}{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{60x + 44}{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{( {2}^{2} \times 3 \times 5)x + {2}^{2} \times 11 }{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{ {2}^{2}( \frac{ {2}^{2} \times 3 \times 5x }{ {2}^{2} } + \frac{ {2}^{2} \times 11 }{ {2}^{2} }) }{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{ {2}^{2}(3 \times 5x + 11) }{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{ {2}^{2}(15x + 11) }{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{15x + 11}{3 \times 5} = \frac{26}{15} \\ \\ \frac{15x + 11}{3 \times 5} = \frac{26}{3 \times 5} \\ \\ 15x + 11 = 26 \\ \\ (15x + 11) + ( - 11) = 26 + ( - 11) \\ \\ 15x + 11 - 11 = 26 - 11 \\ \\ 15x = 15 \\ \\ \frac{15x}{15} = \frac{15}{15} \\ \\ x = 1 [/tex]
[tex]c) \frac{7}{4} - x = \frac{7}{8} \\ \\ \frac{7}{ {2}^{2} } - x = \frac{7}{8} \\ \\ \frac{7 - {(2}^{2})x }{ {2}^{2} } = \frac{7}{8} \\ \\ \frac{7 - 4x}{ {2}^{2} } = \frac{7}{8} \\ \\ \frac{ - 4x + 7}{ {2}^{2} } = \frac{7}{8} \\ \\ \frac{ - 4x + 7}{ {2}^{2} } = \frac{7}{ {2}^{3} } \\ \\ 2( - 4x + 7) = 7 \\ \\ - 2 \times 4x + 2 \times 7 = 7 \\ \\ - 8x + 14 = 7 \\ \\ ( - 8x + 14) + ( - 14) = 7 + ( - 14) \\ \\ - 8x + 14 - 14 = 7 - 14 \\ \\ - 8x = - 7 \\ \\ \frac{8x}{8} = \frac{7}{8} \\ \\ x = \frac{7}{8} [/tex]
[tex]d) \frac{11}{5} - x = \frac{3}{20} \\ \\ \frac{11 - 5x}{5} = \frac{3}{20} \\ \\ \frac{ - 5x + 11}{5} = \frac{3}{20} \\ \\ \frac{ - 5x + 11}{5} = \frac{3}{ {2}^{2} \times 5 } \\ \\ 4( - 5x + 11) = 3 \\ \\ - 4 \times 5x + 4 \times 11 = 3 \\ \\ - 20x + 44 = 3 \\ \\ ( - 20x + 44) + ( - 44) = 3 + ( - 44) \\ \\ - 20x + 44 - 44 = 3 - 44 \\ \\ - 20x = - 41 \\ \\ \frac{20x}{20} = \frac{41}{20} \\ \\ x = \frac{41}{20} [/tex]
[tex]e) \frac{1}{6} - x = \frac{1}{42} \\ \\ \frac{1}{2 \times 3} - x = \frac{1}{42} \\ \\ \frac{1 - (2 \times 3)x}{2 \times 3} = \frac{1}{42} \\ \\ \frac{1 - 6x}{2 \times 3} = \frac{1}{42} \\ \\ \frac{ - 6x + 1}{2 \times 3} = \frac{1}{42} \\ \\ \frac{ - 6x + 1}{2 \times 3} = \frac{1}{2 \times 3 \times 7} \\ \\ 7( - 6x + 1) = 1 \\ \\ - 7 \times 6x + 7 = 1 \\ \\ - 42x + 7 = 1 \\ \\ ( - 42x + 7) + ( - 7) = 1 + ( - 7) \\ \\ - 42x + 7 - 7 = 1 - 7 \\ \\ - 42x = - 6 \\ \\ \frac{42x}{42} = \frac{6}{42} \\ \\ x = \frac{2 \times 3}{2 \times 3 \times 7} \\ \\ x = { \frac{6}{42} }^{(6} \\ \\ x = \frac{1}{7} [/tex]
[tex]b) \frac{5}{12} + x + \frac{19}{60} = \frac{26}{15} \\ \\ \frac{5}{ {2}^{2} \times 3 } + x + \frac{19}{ {2}^{2} \times 3 \times 5} = \frac{26}{15} \\ \\ \frac{5 \times 5 + ( {2}^{2} \times 3 \times 5)x + 19 }{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{25 + (4 \times 3 \times 5)x + 19}{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{25 + 60x + 19}{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{60x + 25 + 19}{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{60x + 44}{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{( {2}^{2} \times 3 \times 5)x + {2}^{2} \times 11 }{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{ {2}^{2}( \frac{ {2}^{2} \times 3 \times 5x }{ {2}^{2} } + \frac{ {2}^{2} \times 11 }{ {2}^{2} }) }{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{ {2}^{2}(3 \times 5x + 11) }{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{ {2}^{2}(15x + 11) }{ {2}^{2} \times 3 \times 5 } = \frac{26}{15} \\ \\ \frac{15x + 11}{3 \times 5} = \frac{26}{15} \\ \\ \frac{15x + 11}{3 \times 5} = \frac{26}{3 \times 5} \\ \\ 15x + 11 = 26 \\ \\ (15x + 11) + ( - 11) = 26 + ( - 11) \\ \\ 15x + 11 - 11 = 26 - 11 \\ \\ 15x = 15 \\ \\ \frac{15x}{15} = \frac{15}{15} \\ \\ x = 1 [/tex]
[tex]c) \frac{7}{4} - x = \frac{7}{8} \\ \\ \frac{7}{ {2}^{2} } - x = \frac{7}{8} \\ \\ \frac{7 - {(2}^{2})x }{ {2}^{2} } = \frac{7}{8} \\ \\ \frac{7 - 4x}{ {2}^{2} } = \frac{7}{8} \\ \\ \frac{ - 4x + 7}{ {2}^{2} } = \frac{7}{8} \\ \\ \frac{ - 4x + 7}{ {2}^{2} } = \frac{7}{ {2}^{3} } \\ \\ 2( - 4x + 7) = 7 \\ \\ - 2 \times 4x + 2 \times 7 = 7 \\ \\ - 8x + 14 = 7 \\ \\ ( - 8x + 14) + ( - 14) = 7 + ( - 14) \\ \\ - 8x + 14 - 14 = 7 - 14 \\ \\ - 8x = - 7 \\ \\ \frac{8x}{8} = \frac{7}{8} \\ \\ x = \frac{7}{8} [/tex]
[tex]d) \frac{11}{5} - x = \frac{3}{20} \\ \\ \frac{11 - 5x}{5} = \frac{3}{20} \\ \\ \frac{ - 5x + 11}{5} = \frac{3}{20} \\ \\ \frac{ - 5x + 11}{5} = \frac{3}{ {2}^{2} \times 5 } \\ \\ 4( - 5x + 11) = 3 \\ \\ - 4 \times 5x + 4 \times 11 = 3 \\ \\ - 20x + 44 = 3 \\ \\ ( - 20x + 44) + ( - 44) = 3 + ( - 44) \\ \\ - 20x + 44 - 44 = 3 - 44 \\ \\ - 20x = - 41 \\ \\ \frac{20x}{20} = \frac{41}{20} \\ \\ x = \frac{41}{20} [/tex]
[tex]e) \frac{1}{6} - x = \frac{1}{42} \\ \\ \frac{1}{2 \times 3} - x = \frac{1}{42} \\ \\ \frac{1 - (2 \times 3)x}{2 \times 3} = \frac{1}{42} \\ \\ \frac{1 - 6x}{2 \times 3} = \frac{1}{42} \\ \\ \frac{ - 6x + 1}{2 \times 3} = \frac{1}{42} \\ \\ \frac{ - 6x + 1}{2 \times 3} = \frac{1}{2 \times 3 \times 7} \\ \\ 7( - 6x + 1) = 1 \\ \\ - 7 \times 6x + 7 = 1 \\ \\ - 42x + 7 = 1 \\ \\ ( - 42x + 7) + ( - 7) = 1 + ( - 7) \\ \\ - 42x + 7 - 7 = 1 - 7 \\ \\ - 42x = - 6 \\ \\ \frac{42x}{42} = \frac{6}{42} \\ \\ x = \frac{2 \times 3}{2 \times 3 \times 7} \\ \\ x = { \frac{6}{42} }^{(6} \\ \\ x = \frac{1}{7} [/tex]
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