Question

linear equations
solving a proportion of the form (x+a)/b = c/d
solve for u.
\\(\frac{3}{4} = \frac{2}{u - 2}\\)
simplify your answer as much as possible.
\\(u = \boxed{}\\)

Explanation:

Step1: Cross - multiply the proportion

Given the equation \(\frac{3}{4}=\frac{2}{u - 2}\), cross - multiplying (which is based on the property of proportions: if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)) gives us \(3\times(u - 2)=4\times2\).

Step2: Expand the left - hand side

Expanding \(3\times(u - 2)\) using the distributive property \(a(b + c)=ab+ac\) (here \(a = 3\), \(b=u\), \(c=- 2\)) gives \(3u-6\). The right - hand side is \(4\times2 = 8\). So our equation becomes \(3u-6 = 8\).

Step3: Solve for \(u\)

First, add 6 to both sides of the equation \(3u-6 = 8\). Adding 6 to both sides: \(3u-6 + 6=8 + 6\), which simplifies to \(3u=14\). Then, divide both sides by 3: \(u=\frac{14}{3}\) (or \(4\frac{2}{3}\)).

Answer:

\(u=\frac{14}{3}\)