Question
Solve for \( x \) \( \begin{array}{l}\frac{2}{x+5}=\frac{-5}{x+3} \\ x=\end{array} \)
Ask by Schneider Kelly. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -\frac{31}{7} \)
Solution
To solve the equation:
\[
\frac{2}{x+5} = \frac{-5}{x+3}
\]
**Step 1: Cross-Multiply**
Multiply both sides of the equation by \((x+5)(x+3)\) to eliminate the denominators:
\[
2(x + 3) = -5(x + 5)
\]
**Step 2: Distribute**
Expand both sides:
\[
2x + 6 = -5x - 25
\]
**Step 3: Combine Like Terms**
Bring all terms involving \(x\) to one side and constant terms to the other:
\[
2x + 5x = -25 - 6
\]
\[
7x = -31
\]
**Step 4: Solve for \(x\)**
Divide both sides by 7:
\[
x = -\frac{31}{7}
\]
**Final Answer:**
\[
x = -\frac{31}{7}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the equation \( \frac{2}{x+5}=\frac{-5}{x+3} \), we can start by cross-multiplying: \[ 2(x + 3) = -5(x + 5). \] Expanding both sides gives: \[ 2x + 6 = -5x - 25. \] Next, we can add \( 5x \) to both sides: \[ 2x + 5x + 6 = -25, \] which simplifies to: \[ 7x + 6 = -25. \] Now, subtract 6 from both sides: \[ 7x = -25 - 6, \] which simplifies to: \[ 7x = -31. \] To solve for \( x \), we divide both sides by 7: \[ x = -\frac{31}{7}. \] Thus, the solution is: \[ x = -\frac{31}{7}. \]
