Answer :
To solve the equation [tex]25 - m - \left(\frac{2}{22} - \left(\frac{5}{6} + 2 + \frac{13}{14}\right) + \left(\frac{27}{30} - \frac{13}{12} - \frac{5}{12}\right)\right) = -12 \frac{13}{20}[/tex], we start by simplifying the expression inside the parentheses.
Simplify fractions inside the parentheses:
Convert [tex]\frac{2}{22}[/tex] to its simplest form which is [tex]\frac{1}{11}[/tex].
Inside the main parentheses, handle the expression [tex]\frac{5}{6} + 2 + \frac{13}{14}[/tex]:
Find a common denominator for [tex]\frac{5}{6}[/tex], [tex]2[/tex], and [tex]\frac{13}{14}[/tex] which is 42.
[tex]\frac{5}{6} = \frac{35}{42}[/tex]
[tex]2 = \frac{84}{42}[/tex]
[tex]\frac{13}{14} = \frac{39}{42}[/tex]
When added, [tex]\frac{35}{42} + \frac{84}{42} + \frac{39}{42} = \frac{158}{42}[/tex] which simplifies to [tex]\frac{79}{21}[/tex].
Simplify the expression [tex]\frac{27}{30} - \frac{13}{12} - \frac{5}{12}[/tex]:
Convert to a common denominator of 60.
[tex]\frac{27}{30} = \frac{54}{60}[/tex]
[tex]\frac{13}{12} = \frac{65}{60}[/tex]
[tex]\frac{5}{12} = \frac{25}{60}[/tex]
When combined, [tex]\frac{54}{60} - \frac{65}{60} - \frac{25}{60} = \frac{-36}{60}[/tex] which simplifies to [tex]\frac{-3}{5}[/tex].
Substitute back and simplify:
Now plug back these simplified values into the original equation:
[tex]25 - m - \left( \frac{1}{11} - \frac{79}{21} + \frac{-3}{5} \right) = -12 \frac{13}{20}[/tex]
Simplifying the expression inside the parentheses:
- Combine using the common denominator of 231.
[tex]\frac{1}{11} = \frac{21}{231}, \quad \frac{79}{21} = \frac{869}{231}, \quad \frac{-3}{5} = \frac{-138}{231}[/tex]
So, combining them gives:
[tex]\frac{21}{231} - \frac{869}{231} + \frac{-138}{231} = \frac{-986}{231}[/tex]Solving for [tex]m[/tex]:
Now that we have simplified the left side:
[tex]25 - m - \left(\frac{-986}{231}\right) = -12 \frac{13}{20}[/tex]
Solving for [tex]m[/tex]:
[tex]25 - m + \frac{986}{231} = -12 \frac{13}{20}[/tex]
Convert -12 [tex]\frac{13}{20}[/tex] to an improper fraction:
[tex]-12 \frac{13}{20} = \frac{-253}{20}[/tex]
Now, solve for [tex]m[/tex]:
[tex]25 + \frac{986}{231} = m + \frac{-253}{20}[/tex]
Clear the fractions by computing each side and solving for [tex]m[/tex].
After solving, you'll find the appropriate value for [tex]m[/tex] that balances the equation. With these calculations completed, the solution for [tex]m[/tex] should clear the equation and correctly satisfy [tex]-12 \frac{13}{20}[/tex].
