To solve the equation ( 1 \frac{11}{24} - x = \frac{7}{16} ), we first convert the mixed number into an improper fraction.
( 1 \frac{11}{24} = \frac{24}{24} + \frac{11}{24} = \frac{35}{24} )
So the equation becomes:
[
\frac{35}{24} - x = \frac{7}{16}
]
Now, we can isolate ( x ):
[
-x = \frac{7}{16} - \frac{35}{24}
]
To subtract these fractions, we need a common denominator. The least common multiple of 16 and 24 is 48.
Convert both fractions to have a denominator of 48:
[
\frac{7}{16} = \frac{7 \times 3}{16 \times 3} = \frac{21}{48}
]
[
\frac{35}{24} = \frac{35 \times 2}{24 \times 2} = \frac{70}{48}
]
Now we can substitute these values back into the equation:
[
-x = \frac{21}{48} - \frac{70}{48}
]
Now perform the subtraction:
[
-x = \frac{21 - 70}{48} = \frac{-49}{48}
]
To isolate ( x ), multiply both sides by -1:
[
x = \frac{49}{48}
]
So the solution is:
[
x = \frac{49}{48}
]
