Question

solve for w.
\\(\frac{w - 5}{2} = \frac{5}{3}\\)
simplify your answer as much as possible.
\\(w = \square\\)

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{w - 5}{2}=\frac{5}{3}\), we cross - multiply. Cross - multiplying gives us \(3(w - 5)=2\times5\).

Step2: Expand the left - hand side

Expanding the left - hand side of the equation \(3(w - 5)=2\times5\), we use the distributive property \(a(b - c)=ab - ac\). Here, \(a = 3\), \(b=w\) and \(c = 5\), so \(3w-15 = 10\).

Step3: Isolate the term with \(w\)

Add 15 to both sides of the equation \(3w-15 = 10\) to isolate the term with \(w\). We get \(3w=10 + 15\).

Step4: Simplify the right - hand side

Simplifying the right - hand side, \(10+15 = 25\), so the equation becomes \(3w=25\).

Step5: Solve for \(w\)

Divide both sides of the equation \(3w = 25\) by 3. We get \(w=\frac{25}{3}\) (or \(8\frac{1}{3}\)).

Answer:

\(w=\frac{25}{3}\) (or \(8\frac{1}{3}\))