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\frac{100}{589019}=|k+23.14|
Expand \frac{1}{5890.19} by multiplying both numerator and the denominator by 100.
|k+23.14|=\frac{100}{589019}
Swap sides so that all variable terms are on the left hand side.
k+23.14=\frac{100}{589019} k+23.14=-\frac{100}{589019}
Use the definition of absolute value.
k=-\frac{681489983}{29450950} k=-\frac{681499983}{29450950}
Subtract 23.14 from both sides of the equation.