Sherman West
06/07/2023 · Senior High School
Solve the proportion and check. \( \frac{-9}{5}=\frac{p}{45} \) The solution set is \( \{\square\} \). (Type an integer or a simplified fraction.)
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Step-by-step Solution
To solve the proportion \( \frac{-9}{5} = \frac{p}{45} \), we can use cross-multiplication.
Cross-multiplying gives us:
\[
-9 \cdot 45 = 5 \cdot p
\]
Calculating the left side:
\[
-9 \cdot 45 = -405
\]
So we have:
\[
-405 = 5p
\]
Next, we solve for \( p \) by dividing both sides by 5:
\[
p = \frac{-405}{5}
\]
Calculating the right side:
\[
p = -81
\]
Thus, the solution set is \( \{-81\} \).
To check our solution, we substitute \( p = -81 \) back into the original proportion:
\[
\frac{-9}{5} = \frac{-81}{45}
\]
Now we simplify \( \frac{-81}{45} \):
The greatest common divisor of 81 and 45 is 9. Dividing both the numerator and the denominator by 9 gives:
\[
\frac{-81 \div 9}{45 \div 9} = \frac{-9}{5}
\]
Since both sides of the equation are equal, our solution is verified.
The final answer is:
\[
\{\text{-81}\}
\]
Quick Answer
The solution set is \{-81\}.
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