To solve for the unknown value in the equation [tex]\(-\frac{192}{256} = \frac{9}{\square}\)[/tex], we need to find the denominator that makes the two fractions equal.
Here are the steps to solve for the unknown denominator:
1. Set up the proportion: The given equation is:
[tex]\[
-\frac{192}{256} = \frac{9}{x}
\][/tex]
where [tex]\( x \)[/tex] is the unknown denominator.
2. Cross-multiply to eliminate the fractions: By cross-multiplying, we multiply the numerator of each fraction by the denominator of the other:
[tex]\[
-192 \cdot x = 256 \cdot 9
\][/tex]
3. Simplify the right-hand side: Perform the multiplication on the right-hand side:
[tex]\[
256 \cdot 9 = 2304
\][/tex]
So the equation becomes:
[tex]\[
-192 \cdot x = 2304
\][/tex]
4. Solve for [tex]\( x \)[/tex]: To isolate [tex]\( x \)[/tex], divide both sides of the equation by [tex]\(-192\)[/tex]:
[tex]\[
x = \frac{2304}{-192}
\][/tex]
5. Perform the division: Finally, divide 2304 by [tex]\(-192\)[/tex]:
[tex]\[
x = -12
\][/tex]
So the value of the unknown denominator is [tex]\(-12\)[/tex].
The unknown value that makes the equation true is [tex]\(-12\)[/tex].
