Mathematics

Question

3/7 x + 5/8 - 3/14 x + 1/4
3/7 x + 5/8 - 3/14 x + 1/4

1 Answer

  • [tex] \frac{3}{7} x + \frac{5}{8} - \frac{3}{14}x + \frac{1}{4} =[/tex]
    [tex] \frac{3}{7} x - \frac{3}{14} x = - \frac{5}{8} -\frac{1}{4}[/tex]

    MMC (7,8,14,4)

    7,8,14,4 | 2
    7, 4, 7, 2| 2
    7, 2, 7, 1| 2
    7, 1, 7, 1| 7
    1, 1, 1, 1____ 2*2*2*7 = 56

    Solving
    [tex] \frac{3}{7} x - \frac{3}{14} x = - \frac{5}{8} - \frac{1}{4}[/tex]
    [tex]\frac{(56\div7*3)}{56} x - \frac{(56\div14*3)}{56} x = - \frac{(56\div8*5)}{56} -\frac{(56\div4*1)}{56}[/tex]
    [tex] \frac{24}{56}x - \frac{12}{56} x = - \frac{35}{56} - \frac{14}{56} [/tex]
    Cancel the denominators (56)
    [tex]24x - 12x = - 35 - 14[/tex]
    [tex]12x = - 49[/tex]
    [tex]\boxed{x = - \frac{49}{12}}[/tex]
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