Thank you for visiting Given the function tex f x 4 x 5 3 tex for what values of tex x tex is tex f x 15 tex A. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To solve for $x$ in
$$
4|x-5| + 3 = 15,
$$
follow these steps:
1. Subtract 3 from both sides to isolate the absolute value term:
$$
4|x-5| = 15 - 3 \quad \Rightarrow \quad 4|x-5| = 12.
$$
2. Divide both sides by 4:
$$
|x-5| = \frac{12}{4} \quad \Rightarrow \quad |x-5| = 3.
$$
3. Recall that if $|A| = B$, then $A = B$ or $A = -B$. Therefore, set up the two equations:
$$
x - 5 = 3 \quad \text{or} \quad x - 5 = -3.
$$
4. Solve each equation:
- For $x - 5 = 3$:
$$
x = 5 + 3 \quad \Rightarrow \quad x = 8.
$$
- For $x - 5 = -3$:
$$
x = 5 - 3 \quad \Rightarrow \quad x = 2.
$$
Thus, the values of $x$ that satisfy the equation are $x = 2$ and $x = 8$.
$$
4|x-5| + 3 = 15,
$$
follow these steps:
1. Subtract 3 from both sides to isolate the absolute value term:
$$
4|x-5| = 15 - 3 \quad \Rightarrow \quad 4|x-5| = 12.
$$
2. Divide both sides by 4:
$$
|x-5| = \frac{12}{4} \quad \Rightarrow \quad |x-5| = 3.
$$
3. Recall that if $|A| = B$, then $A = B$ or $A = -B$. Therefore, set up the two equations:
$$
x - 5 = 3 \quad \text{or} \quad x - 5 = -3.
$$
4. Solve each equation:
- For $x - 5 = 3$:
$$
x = 5 + 3 \quad \Rightarrow \quad x = 8.
$$
- For $x - 5 = -3$:
$$
x = 5 - 3 \quad \Rightarrow \quad x = 2.
$$
Thus, the values of $x$ that satisfy the equation are $x = 2$ and $x = 8$.
Thank you for reading the article Given the function tex f x 4 x 5 3 tex for what values of tex x tex is tex f x 15 tex A. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
