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Which value of x satisfies the equation (4)/(5)(x-(1)/(4))=-(21)/(5) ? 5 6 -6 -5

Which value of x x satisfies the equation 45(x−14)=−215 \frac{4}{5}\left(x-\frac{1}{4}\right)=-\frac{21}{5} ?\newline55\newline66\newline−6 -6 \newline−5 -5

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Full solution

Q. Which value of x x satisfies the equation 45(x−14)=−215 \frac{4}{5}\left(x-\frac{1}{4}\right)=-\frac{21}{5} ?\newline55\newline66\newline−6 -6 \newline−5 -5
  1. Write Equation: Write down the equation.\newline(45)(x−14)=−215(\frac{4}{5})(x - \frac{1}{4}) = -\frac{21}{5}
  2. Multiply by 54\frac{5}{4}: Multiply both sides of the equation by 54\frac{5}{4} to isolate the term with xx.\left(\frac{\(5\)}{\(4\)}\right) \times \left(\frac{\(4\)}{\(5\)}\right)(x - \frac{\(1\)}{\(4\)}) = \left(\frac{\(5\)}{\(4\)}\right) \times \left(-\frac{\(21\)}{\(5\)}\right)
  3. Simplify Left Side: Simplify both sides of the equation.\(\newlineThe 54\frac{5}{4} and 45\frac{4}{5} on the left side cancel each other out, leaving us with:\newlinex−14=−215×54x - \frac{1}{4} = -\frac{21}{5} \times \frac{5}{4}
  4. Calculate Right Side: Calculate the right side of the equation.\newline−215×54=−21×14=−214-\frac{21}{5} \times \frac{5}{4} = -21 \times \frac{1}{4} = -\frac{21}{4}
  5. Add 14\frac{1}{4}: Add 14\frac{1}{4} to both sides of the equation to solve for xx.x−14+14=−214+14x - \frac{1}{4} + \frac{1}{4} = -\frac{21}{4} + \frac{1}{4}
  6. Simplify Equation: Simplify the equation. x=−214+14x = -\frac{21}{4} + \frac{1}{4}
  7. Combine Fractions: Combine the fractions on the right side of the equation.\newlinex=−21+14x = \frac{-21 + 1}{4}\newlinex=−204x = \frac{-20}{4}
  8. Final Simplification: Simplify the fraction. x=−5x = -5

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