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Solve for x and write your answer in simplest form. -x=x+(3)/(5)(4x-(1)/(3))+1 Answer: x=

Solve for x x and write your answer in simplest form.\newline−x=x+35(4x−13)+1 -x=x+\frac{3}{5}\left(4 x-\frac{1}{3}\right)+1 \newlineAnswer: x= x=

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Full solution

Q. Solve for x x and write your answer in simplest form.\newline−x=x+35(4x−13)+1 -x=x+\frac{3}{5}\left(4 x-\frac{1}{3}\right)+1 \newlineAnswer: x= x=
  1. Write Equation: First, let's write down the equation given:\newline−x=x+(35)(4x−13)+1-x = x + \left(\frac{3}{5}\right)(4x - \frac{1}{3}) + 1
  2. Distribute Terms: Now, distribute the (35)(\frac{3}{5}) across the terms inside the parentheses: -x = x + (\frac{\(3\)}{\(5\)})\cdot\(4x - (\frac{33}{55})\cdot(\frac{11}{33}) + 11
  3. Simplify Distributed Terms: Simplify the distributed terms: −x=x+(125)x−(315)+1-x = x + \left(\frac{12}{5}\right)x - \left(\frac{3}{15}\right) + 1
  4. Simplify Fraction: Simplify the fraction (315)(\frac{3}{15}) to (15)(\frac{1}{5}):-x = x + (\frac{\(12\)}{\(5\)})x - \frac{\(1\)}{\(5\)} + \(1
  5. Combine Like Terms: Combine like terms on the right side of the equation: −x=(175)x−15+1-x = \left(\frac{17}{5}\right)x - \frac{1}{5} + 1
  6. Convert Whole Number: Convert the whole number 11 to a fraction with a denominator of 55 to combine with −15-\frac{1}{5}:−x=(175)x−15+55-x = (\frac{17}{5})x - \frac{1}{5} + \frac{5}{5}
  7. Combine Fractions: Combine the fractions on the right side: −x=(175)x+45-x = \left(\frac{17}{5}\right)x + \frac{4}{5}
  8. Add xx to Both Sides: Add xx to both sides to get all xx terms on one side:\newline0=(175)x+x+450 = \left(\frac{17}{5}\right)x + x + \frac{4}{5}
  9. Convert Whole Number xx: Convert the whole number xx to a fraction with a denominator of 55 to combine with (175)x(\frac{17}{5})x:0=(175)x+(55)x+450 = \left(\frac{17}{5}\right)x + \left(\frac{5}{5}\right)x + \frac{4}{5}
  10. Combine xx Terms: Combine the xx terms:\newline0=(225)x+450 = \left(\frac{22}{5}\right)x + \frac{4}{5}
  11. Subtract 45\frac{4}{5}: Subtract 45\frac{4}{5} from both sides to isolate the xx term:\newline-\left(\frac{\(4\)}{\(5\)}\right) = \left(\frac{\(22\)}{\(5\)}\right)x
  12. Divide by \(\frac{22}{5}: Divide both sides by 225\frac{22}{5} to solve for x:\newline−45/225=x-\frac{4}{5} / \frac{22}{5} = x
  13. Multiply by Reciprocal: Multiply by the reciprocal of (225)(\frac{22}{5}) to simplify the division: -\left(\frac{\(4\)}{\(5\)}\right) \cdot \left(\frac{\(5\)}{\(22\)}\right) = x
  14. Simplify Multiplication: Simplify the multiplication: \(x = -\frac{20}{110}
  15. Reduce Fraction: Reduce the fraction −20110-\frac{20}{110} to its simplest form:\newlinex=−211x = -\frac{2}{11}

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