Question

1. \\(\frac{12}{18} = \frac{3x + 4}{15}\\)

Explanation:

Step1: Cross - multiply the proportion

We have the equation \(\frac{12}{18}=\frac{3x + 4}{15}\). By the property of proportions (cross - multiplication: if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)), we get \(12\times15 = 18\times(3x + 4)\).
Calculating the left - hand side: \(12\times15=180\).
Calculating the right - hand side: \(18\times(3x + 4)=18\times3x+18\times4 = 54x+72\).
So the equation becomes \(180=54x + 72\).

Step2: Isolate the term with \(x\)

Subtract 72 from both sides of the equation \(180 = 54x+72\).
\(180-72=54x+72 - 72\).
Calculating the left - hand side: \(180 - 72 = 108\).
The equation simplifies to \(108 = 54x\).

Step3: Solve for \(x\)

Divide both sides of the equation \(108 = 54x\) by 54.
\(\frac{108}{54}=\frac{54x}{54}\).
Since \(\frac{108}{54} = 2\) and \(\frac{54x}{54}=x\), we get \(x = 2\).

Answer:

\(x = 2\)