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Mathematics
1 2 x + 13 = 9 (1)/(2)x+13=9
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To solve the equation 1 2 x + 13 = 9 (1)/(2)x+13=9, we can follow these steps:
  1. Subtract 13 from both sides of the equation to isolate the term with x:
    1 2 x = 9 13 (1)/(2)x=9-13
    Simplifying the right side gives: 1 2 x = 4 (1)/(2)x=-4
  2. To get rid of the fraction 1 2 (1)/(2), we can multiply both sides of the equation by its reciprocal, which is 2:
    2 1 2 x = 2 ( 4 ) 2*(1)/(2)x=2*(-4)
    Simplifying gives: x = 8 x=-8
    So the solution to the equation 1 2 x + 13 = 9 (1)/(2)x+13=9 is x = 8 x=-8.
    Therefore, to solve equations with fractions, we need to eliminate the fraction by multiplying both sides of the equation by the reciprocal of the fraction. This will simplify the equation and make it easier to solve for the variable. Furthermore, we always have to check our solutions by substituting them back into the original equation to make sure they are valid.
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