Question

assignment 2.2 linear equations in one variable
score: 7/13 answered: 7/13
question 8
solve the equation. enter an exact answer. if there is no solution, enter dne
\\(\frac{3}{w + 5} + 2 = \frac{4}{w + 5}\\)
\\(w = \\)
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Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation \(\frac{3}{w + 5}+2=\frac{4}{w + 5}\) by \(w + 5\) (note that \(w
eq - 5\) to avoid division by zero) to get \(3+2(w + 5)=4\).

Step2: Expand and simplify

Expand the left - hand side: \(3 + 2w+10 = 4\). Combine like terms: \(2w+13 = 4\).

Step3: Solve for \(w\)

Subtract 13 from both sides: \(2w=4 - 13=-9\). Then divide both sides by 2: \(w =-\frac{9}{2}\).
We need to check if this solution makes the original denominator zero. Substitute \(w =-\frac{9}{2}\) into \(w + 5\), we get \(-\frac{9}{2}+5=\frac{1}{2}
eq0\). So the solution is valid.

Answer:

\(w =-\frac{9}{2}\)