Question

solve each proportion.

1. \\(\frac{k - 4}{5k + 11} = \frac{8}{9}\\)

Explanation:

Step1: Cross - multiply the proportion

Given the proportion \(\frac{k - 4}{5k+11}=\frac{8}{9}\), by the cross - multiplication property of proportions (if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)), we get:
\(9(k - 4)=8(5k + 11)\)

Step2: Expand both sides

Expand the left - hand side: \(9\times k-9\times4 = 9k-36\)
Expand the right - hand side: \(8\times5k+8\times11=40k + 88\)
So the equation becomes \(9k-36 = 40k+88\)

Step3: Move the terms with \(k\) to one side and constants to the other

Subtract \(9k\) from both sides: \(9k-9k - 36=40k-9k + 88\), which simplifies to \(-36 = 31k+88\)
Then subtract 88 from both sides: \(-36-88=31k+88 - 88\), so \(-124 = 31k\)

Step4: Solve for \(k\)

Divide both sides by 31: \(k=\frac{-124}{31}=- 4\)

Answer:

\(k = - 4\)