1 11/24-x=7/16

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:

\[ x = \frac{49}{48} \]