Wyatt Conner
08/20/2023 · Elementary School
12) \( \frac{10}{x+6}=\frac{9}{x+8} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the equation
\[
\frac{10}{x+6} = \frac{9}{x+8},
\]
we can cross-multiply to eliminate the fractions. This gives us:
\[
10(x + 8) = 9(x + 6).
\]
Now, we will distribute both sides:
\[
10x + 80 = 9x + 54.
\]
Next, we will isolate \(x\) by subtracting \(9x\) from both sides:
\[
10x - 9x + 80 = 54,
\]
which simplifies to:
\[
x + 80 = 54.
\]
Now, subtract 80 from both sides:
\[
x = 54 - 80,
\]
which simplifies to:
\[
x = -26.
\]
Thus, the solution to the equation is
\[
\boxed{-26}.
\]
Quick Answer
The solution to the equation is \( x = -26 \).
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