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Express your answer as a proper or improper fraction (4)/(11)x+(1)/(4)=(1)/(8)

Express your answer as a proper or improper fraction\newline411x+14=18 \frac{4}{11} x+\frac{1}{4}=\frac{1}{8}

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Multiply and divide powers: variable basesright chevron icon

Full solution

Q. Express your answer as a proper or improper fraction\newline411x+14=18 \frac{4}{11} x+\frac{1}{4}=\frac{1}{8}
  1. Isolate x term: Isolate the term containing xx on one side of the equation.\newlineTo do this, we need to subtract 14\frac{1}{4} from both sides of the equation to get the term with xx by itself.\newline411x+14−14=18−14\frac{4}{11}x + \frac{1}{4} - \frac{1}{4} = \frac{1}{8} - \frac{1}{4}
  2. Simplify after subtraction: Simplify both sides of the equation after subtraction.\newlineOn the left side, (14)−(14)(\frac{1}{4}) - (\frac{1}{4}) cancels out, leaving us with (411)x(\frac{4}{11})x. On the right side, we need to find a common denominator to subtract (14)(\frac{1}{4}) from (18)(\frac{1}{8}). The common denominator for 44 and 88 is 88.\newline(411)x=(18)−(28)(\frac{4}{11})x = (\frac{1}{8}) - (\frac{2}{8})
  3. Continue simplifying: Continue simplifying the right side of the equation.\newlineSubtracting (28)(\frac{2}{8}) from (18)(\frac{1}{8}) gives us (−18)(-\frac{1}{8}).\newline(411)x=−(18)(\frac{4}{11})x = -(\frac{1}{8})
  4. Multiply by reciprocal: Solve for xx by multiplying both sides of the equation by the reciprocal of (411)(\frac{4}{11}). The reciprocal of (411)(\frac{4}{11}) is (114)(\frac{11}{4}). We multiply both sides by (114)(\frac{11}{4}) to isolate xx. (114)×(411)x=(114)×−(18)(\frac{11}{4}) \times (\frac{4}{11})x = (\frac{11}{4}) \times -(\frac{1}{8})
  5. Simplify both sides: Simplify both sides of the equation.\newlineOn the left side, (114)×(411)(\frac{11}{4}) \times (\frac{4}{11}) simplifies to 11, leaving us with xx. On the right side, we multiply the numerators and the denominators separately.\newlinex=11×−14×8x = \frac{11 \times -1}{4 \times 8}
  6. Finish calculation: Finish the calculation on the right side to find the value of xx.x=−1132x = \frac{-11}{32}

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