Question

solve for x.
\\(\frac{4}{5} = \frac{6}{x + 2}\\)
simplify your answer as much as possible
\\(x = \square\\)

Explanation:

Step1: Cross - multiply the fractions

To solve the equation \(\frac{4}{5}=\frac{6}{x + 2}\), we use cross - multiplication. Cross - multiplication states that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\).
Applying this to our equation, we get \(4\times(x + 2)=5\times6\).

Step2: Expand and simplify the equation

First, expand the left - hand side: \(4x+8 = 30\).
Then, subtract 8 from both sides of the equation: \(4x+8 - 8=30 - 8\), which simplifies to \(4x=22\).

Step3: Solve for x

Divide both sides of the equation \(4x = 22\) by 4: \(x=\frac{22}{4}\).
Simplify the fraction \(\frac{22}{4}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \(x=\frac{11}{2}=5.5\).

Answer:

\(x = \frac{11}{2}\) (or \(x = 5.5\))