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Evaluate w+(-x)-(2)/(3) where w=-(5)/(9) and x=(4)/(3).

Evaluate w+(−x)−23 w+(-x)-\frac{2}{3} where w=−59 w=-\frac{5}{9} and x=43 x=\frac{4}{3} .

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Full solution

Q. Evaluate w+(−x)−23 w+(-x)-\frac{2}{3} where w=−59 w=-\frac{5}{9} and x=43 x=\frac{4}{3} .
  1. Substitute Values: Substitute the given values of ww and xx into the expression.\newlineWe have w=−(59)w = -\left(\frac{5}{9}\right) and x=(43)x = \left(\frac{4}{3}\right). The expression becomes:\newlinew+(−x)−(23)=(−(59))+(−(43))−(23)w + (-x) - \left(\frac{2}{3}\right) = \left(-\left(\frac{5}{9}\right)\right) + \left(-\left(\frac{4}{3}\right)\right) - \left(\frac{2}{3}\right)
  2. Combine Like Terms: Simplify the expression by combining like terms.\newlineFirst, we need to add the two negative terms together. Since they have different denominators, we need to find a common denominator, which is 99 in this case.\newline(−(5/9))+(−(4/3))=(−(5/9))+(−(4/3×3/3))=(−(5/9))+(−(12/9))(-(5/9)) + (-(4/3)) = (-(5/9)) + (-(4/3 \times 3/3)) = (-(5/9)) + (-(12/9))\newlineNow we can add them together:\newline(−(5/9))+(−(12/9))=−(5/9+12/9)=−(17/9)(-(5/9)) + (-(12/9)) = -(5/9 + 12/9) = -(17/9)
  3. Subtract from Result: Subtract (23)(\frac{2}{3}) from the result obtained in Step 22.\newlineWe need to convert (23)(\frac{2}{3}) to have the same denominator as (179)(\frac{17}{9}) before we can subtract. The common denominator is 99.\newline(23)=(23×33)=(69)(\frac{2}{3}) = (\frac{2}{3} \times \frac{3}{3}) = (\frac{6}{9})\newlineNow subtract (69)(\frac{6}{9}) from −(179)-(\frac{17}{9}):\newline−(179)−(69)=−(179+69)=−(239)-(\frac{17}{9}) - (\frac{6}{9}) = -(\frac{17}{9} + \frac{6}{9}) = -(\frac{23}{9})
  4. Write Final Answer: Write the final answer.\newlineThe simplified expression is −239-\frac{23}{9}.

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