Question

solve each of the following proportions.

1. \\(\frac{3}{x - 4}=\frac{7}{x}\\)

5.

Explanation:

Step1: Cross - multiply the proportion

To solve the proportion \(\frac{3}{x - 4}=\frac{7}{x}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\).
Applying this property to our proportion, we get \(3\times x=(x - 4)\times7\).

Step2: Expand the right - hand side

Expand the right - hand side of the equation \(3x = 7(x - 4)\). Using the distributive property \(a(b - c)=ab - ac\), we have \(3x=7x-28\).

Step3: Isolate the variable \(x\)

Subtract \(3x\) from both sides of the equation:
\(3x-3x=7x - 3x-28\)
\(0 = 4x-28\)
Then add 28 to both sides:
\(0 + 28=4x-28 + 28\)
\(28 = 4x\)

Step4: Solve for \(x\)

Divide both sides of the equation \(28 = 4x\) by 4:
\(x=\frac{28}{4}=7\)

Answer:

\(x = 7\)