Question

solve the proportion.
\\(\frac{3}{4} = \frac{6}{x + 4}\\)

\\(x = \square\\) (type an integer or a simplified fraction.)

Explanation:

Step1: Cross - multiply the proportion

To solve the proportion \(\frac{3}{4}=\frac{6}{x + 4}\), 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 \(3\times(x + 4)=4\times6\).

Step2: Simplify both sides of the equation

First, simplify the left - hand side: \(3\times(x + 4)=3x+12\) (using the distributive property \(a(b + c)=ab+ac\) where \(a = 3\), \(b=x\) and \(c = 4\)).
Simplify the right - hand side: \(4\times6 = 24\). So our equation becomes \(3x+12 = 24\).

Step3: Solve for x

Subtract 12 from both sides of the equation: \(3x+12-12=24 - 12\).
This simplifies to \(3x=12\).
Then divide both sides by 3: \(\frac{3x}{3}=\frac{12}{3}\).

Step4: Find the value of x

Simplifying \(\frac{3x}{3}=\frac{12}{3}\), we get \(x = 4\).

Answer:

\(x = 4\)