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\frac{4}{5}x=-\frac{1}{5}
Subtract \frac{1}{5} from both sides. Anything subtracted from zero gives its negation.
x=-\frac{1}{5}\times \frac{5}{4}
Multiply both sides by \frac{5}{4}, the reciprocal of \frac{4}{5}.
x=\frac{-5}{5\times 4}
Multiply -\frac{1}{5} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.
x=\frac{-1}{4}
Cancel out 5 in both numerator and denominator.
x=-\frac{1}{4}
Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.