Question
20. Given \( f(x)=2 x+9 \), if \( f(x)=15 \), find \( x \). \( \begin{aligned} f(15) & =2(15)+9 \\ & =30+9 \\ & =39\end{aligned} \)
Ask by Floyd Barrett. in Guam
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 3 \)
Solution
To solve the problem, we need to find the value of \( x \) such that \( f(x) = 15 \) given the function \( f(x) = 2x + 9 \).
1. Start with the equation:
\[
f(x) = 15
\]
This means:
\[
2x + 9 = 15
\]
2. Next, we will isolate \( x \) by subtracting 9 from both sides:
\[
2x = 15 - 9
\]
Simplifying the right side gives:
\[
2x = 6
\]
3. Now, divide both sides by 2 to solve for \( x \):
\[
x = \frac{6}{2}
\]
This simplifies to:
\[
x = 3
\]
Thus, the value of \( x \) such that \( f(x) = 15 \) is \( \boxed{3} \).
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Simplify this solution Beyond the Answer
To solve for \( x \) when \( f(x) = 15 \), you start with the equation \( 2x + 9 = 15 \). Subtracting 9 from both sides gives \( 2x = 6 \). Dividing by 2 results in \( x = 3 \). So, when \( f(x) = 15 \), the value of \( x \) is 3. Now, let's take a moment to appreciate linear functions like this: they're like the straight roads of mathematics! Once you get the hang of them, solving for \( x \) becomes as easy as riding a bicycle downhill—smooth sailing!
