Question

solve for w.
\\(\frac{w + 5}{2} = \frac{w + 4}{3}\\)
there may be 1 or 2 solutions.
\\(w = \square\\) or \\(w = \square\\)

Explanation:

Step1: Cross - multiply to eliminate denominators

To solve the equation \(\frac{w + 5}{2}=\frac{w + 4}{3}\), we cross - multiply. Cross - multiplying gives us \(3(w + 5)=2(w + 4)\). The reason for cross - multiplying is that if \(\frac{a}{b}=\frac{c}{d}\) (where \(b
eq0\) and \(d
eq0\)), then \(ad = bc\).

Step2: Expand both sides

Expanding the left - hand side: \(3\times w+3\times5 = 3w + 15\). Expanding the right - hand side: \(2\times w+2\times4=2w + 8\). So our equation becomes \(3w + 15=2w + 8\).

Step3: Solve for \(w\)

Subtract \(2w\) from both sides of the equation: \(3w-2w + 15=2w-2w + 8\), which simplifies to \(w + 15=8\). Then subtract 15 from both sides: \(w+15 - 15=8 - 15\), so \(w=-7\). Since this is a linear equation (degree 1), there is only one solution.

Answer:

\(w = - 7\) (Note: The statement "There may be 1 or 2 solutions" is incorrect for this linear equation. The equation \(\frac{w + 5}{2}=\frac{w + 4}{3}\) is a linear equation in one variable, and it has exactly one solution \(w=-7\).)