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Evaluate 
1+(-(2)/(3))-(-m) where 
m=(9)/(2).

Evaluate 1+(23)(m) 1+\left(-\frac{2}{3}\right)-(-m) where m=92 m=\frac{9}{2} .

Full solution

Q. Evaluate 1+(23)(m) 1+\left(-\frac{2}{3}\right)-(-m) where m=92 m=\frac{9}{2} .
  1. Substitute Value into Expression: Substitute the value of mm into the expression.\newlineWe are given m=92m = \frac{9}{2}. We need to substitute this value into the expression 1+(23)(m)1 + \left(-\frac{2}{3}\right) - \left(-m\right).\newlineExpression after substitution: 1+(23)(92)1 + \left(-\frac{2}{3}\right) - \left(-\frac{9}{2}\right)
  2. Simplify Negative Signs: Simplify the negative signs.\newlineWe have two negative signs in the expression, which means we will be subtracting the negative values, effectively adding their positive counterparts.\newlineSimplified expression: 1(23)+(92)1 - \left(\frac{2}{3}\right) + \left(\frac{9}{2}\right)
  3. Find Common Denominator: Find a common denominator to combine the fractions.\newlineThe common denominator for 33 and 22 is 66. We will convert both fractions to have the denominator of 66.\newline(23)(\frac{2}{3}) becomes (46)(\frac{4}{6}) and (92)(\frac{9}{2}) becomes (276)(\frac{27}{6}).\newlineExpression with common denominator: 1(46)+(276)1 - (\frac{4}{6}) + (\frac{27}{6})
  4. Combine Fractions: Combine the fractions.\newlineNow that we have a common denominator, we can combine the fractions by subtracting and adding their numerators.\newline(276)(46)=(236)(\frac{27}{6}) - (\frac{4}{6}) = (\frac{23}{6})\newlineExpression combined: 1+(236)1 + (\frac{23}{6})
  5. Convert Whole Number to Fraction: Convert the whole number to a fraction with the same denominator to combine with the fraction part.\newline11 can be written as (66)(\frac{6}{6}) to have the same denominator as (236)(\frac{23}{6}).\newlineExpression with whole number as fraction: (66)+(236)(\frac{6}{6}) + (\frac{23}{6})
  6. Combine Whole Number with Fraction: Combine the whole number fraction with the fraction part.\newlineNow we can add the numerators since the denominators are the same.\newline(66)+(236)=(296)(\frac{6}{6}) + (\frac{23}{6}) = (\frac{29}{6})

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