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Evaluate 
-(2)/(5)-x+(-(9)/(10)) where 
x=(4)/(5).

Evaluate 25x+(910) -\frac{2}{5}-x+\left(-\frac{9}{10}\right) where x=45 x=\frac{4}{5} .

Full solution

Q. Evaluate 25x+(910) -\frac{2}{5}-x+\left(-\frac{9}{10}\right) where x=45 x=\frac{4}{5} .
  1. Substitute x value: Substitute the value of xx into the expression.\newlineWe are given x=45x = \frac{4}{5}, so we will replace xx in the expression with 45\frac{4}{5}.\newlineExpression: 2545+(910)-\frac{2}{5} - \frac{4}{5} + \left(-\frac{9}{10}\right)
  2. Combine fractions: Combine the fractions with a common denominator.\newlineThe fractions 25-\frac{2}{5} and 45-\frac{4}{5} already have a common denominator of 55, so we can combine them directly. The fraction 910-\frac{9}{10} has a different denominator, so we will need to find a common denominator for all fractions.\newlineCommon denominator for 55 and 1010 is 1010.
  3. Convert to common denominator: Convert the fractions to have the common denominator.\newline25-\frac{2}{5} becomes 410-\frac{4}{10} when we multiply both the numerator and the denominator by 22.\newline45-\frac{4}{5} becomes 810-\frac{8}{10} when we multiply both the numerator and the denominator by 22.\newlineNow we have: 410-\frac{4}{10} - 810\frac{8}{10} + 910-\frac{9}{10}
  4. Add fractions: Add the fractions together.\newlineNow that all fractions have the same denominator, we can add their numerators.\newline410810910=4+8+910-\frac{4}{10} - \frac{8}{10} - \frac{9}{10} = -\frac{4 + 8 + 9}{10}\newlineCalculate the sum of the numerators: 4+8+9=214 + 8 + 9 = 21\newlineSo, we have: 2110-\frac{21}{10}
  5. Simplify expression: Simplify the expression.\newlineThe negative sign in front of the fraction means we are taking the negative of the entire fraction.\newlineTherefore, the simplified expression is: 2110-\frac{21}{10}