Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To solve the equation [tex]\(\frac{1}{3}|x - 3| + 4 = 10\)[/tex], we need to isolate the absolute value expression and then consider the different cases it presents. Let's go through the solution step-by-step.
1. Subtract 4 from both sides to isolate the absolute value term:
[tex]\[ \frac{1}{3}|x - 3| + 4 - 4 = 10 - 4 \][/tex]
[tex]\[ \frac{1}{3}|x - 3| = 6 \][/tex]
2. Multiply both sides by 3 to eliminate the fraction:
[tex]\[ 3 \cdot \frac{1}{3}|x - 3| = 6 \cdot 3 \][/tex]
[tex]\[ |x - 3| = 18 \][/tex]
3. Consider the two cases for the absolute value expression:
[tex]\[ x - 3 = 18 \quad \text{or} \quad x - 3 = -18 \][/tex]
4. Solve each case separately:
- For [tex]\(x - 3 = 18\)[/tex]:
[tex]\[ x = 18 + 3 \][/tex]
[tex]\[ x = 21 \][/tex]
- For [tex]\(x - 3 = -18\)[/tex]:
[tex]\[ x = -18 + 3 \][/tex]
[tex]\[ x = -15 \][/tex]
Therefore, the solutions to the equation are [tex]\(x = -15\)[/tex] and [tex]\(x = 21\)[/tex].
Thus, the correct answer from the choices provided is:
- [tex]\( x = -15 \)[/tex] and [tex]\( x = 21 \)[/tex]
So, the correct choice is:
[tex]\[ \boxed{x = -15 \text{ and } x = 21} \][/tex]
1. Subtract 4 from both sides to isolate the absolute value term:
[tex]\[ \frac{1}{3}|x - 3| + 4 - 4 = 10 - 4 \][/tex]
[tex]\[ \frac{1}{3}|x - 3| = 6 \][/tex]
2. Multiply both sides by 3 to eliminate the fraction:
[tex]\[ 3 \cdot \frac{1}{3}|x - 3| = 6 \cdot 3 \][/tex]
[tex]\[ |x - 3| = 18 \][/tex]
3. Consider the two cases for the absolute value expression:
[tex]\[ x - 3 = 18 \quad \text{or} \quad x - 3 = -18 \][/tex]
4. Solve each case separately:
- For [tex]\(x - 3 = 18\)[/tex]:
[tex]\[ x = 18 + 3 \][/tex]
[tex]\[ x = 21 \][/tex]
- For [tex]\(x - 3 = -18\)[/tex]:
[tex]\[ x = -18 + 3 \][/tex]
[tex]\[ x = -15 \][/tex]
Therefore, the solutions to the equation are [tex]\(x = -15\)[/tex] and [tex]\(x = 21\)[/tex].
Thus, the correct answer from the choices provided is:
- [tex]\( x = -15 \)[/tex] and [tex]\( x = 21 \)[/tex]
So, the correct choice is:
[tex]\[ \boxed{x = -15 \text{ and } x = 21} \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.