Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To solve for the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( f(x) = 18 \)[/tex] given the function [tex]\( f(x) = 3|x-2| + 6 \)[/tex], we should follow these steps:
1. Set up the equation: Start by setting the function equal to 18.
[tex]\[ 3|x-2| + 6 = 18 \][/tex]
2. Isolate the absolute value term: Subtract 6 from both sides to isolate the term with the absolute value.
[tex]\[ 3|x-2| = 18 - 6 \][/tex]
[tex]\[ 3|x-2| = 12 \][/tex]
3. Solve for the absolute value: Divide both sides by 3.
[tex]\[ |x-2| = \frac{12}{3} \][/tex]
[tex]\[ |x-2| = 4 \][/tex]
4. Solve the absolute value equation: Recall that [tex]\( |a| = b \)[/tex] has two solutions [tex]\( a = b \)[/tex] and [tex]\( a = -b \)[/tex]. Apply this to the equation [tex]\( |x-2| = 4 \)[/tex].
[tex]\[ x - 2 = 4 \quad \text{or} \quad x - 2 = -4 \][/tex]
5. Solve each equation for [tex]\( x \)[/tex]:
[tex]\[ x - 2 = 4 \quad \Rightarrow \quad x = 4 + 2 = 6 \][/tex]
[tex]\[ x - 2 = -4 \quad \Rightarrow \quad x = -4 + 2 = -2 \][/tex]
6. Conclusion: The values of [tex]\( x \)[/tex] that satisfy [tex]\( f(x) = 18 \)[/tex] are [tex]\( x = 6 \)[/tex] and [tex]\( x = -2 \)[/tex].
Thus, the correct values of [tex]\( x \)[/tex] are:
[tex]\[\boxed{-2 \text{ and } 6}\][/tex]
So, the answer is:
[tex]\[ x = -2, x = 6 \][/tex]
1. Set up the equation: Start by setting the function equal to 18.
[tex]\[ 3|x-2| + 6 = 18 \][/tex]
2. Isolate the absolute value term: Subtract 6 from both sides to isolate the term with the absolute value.
[tex]\[ 3|x-2| = 18 - 6 \][/tex]
[tex]\[ 3|x-2| = 12 \][/tex]
3. Solve for the absolute value: Divide both sides by 3.
[tex]\[ |x-2| = \frac{12}{3} \][/tex]
[tex]\[ |x-2| = 4 \][/tex]
4. Solve the absolute value equation: Recall that [tex]\( |a| = b \)[/tex] has two solutions [tex]\( a = b \)[/tex] and [tex]\( a = -b \)[/tex]. Apply this to the equation [tex]\( |x-2| = 4 \)[/tex].
[tex]\[ x - 2 = 4 \quad \text{or} \quad x - 2 = -4 \][/tex]
5. Solve each equation for [tex]\( x \)[/tex]:
[tex]\[ x - 2 = 4 \quad \Rightarrow \quad x = 4 + 2 = 6 \][/tex]
[tex]\[ x - 2 = -4 \quad \Rightarrow \quad x = -4 + 2 = -2 \][/tex]
6. Conclusion: The values of [tex]\( x \)[/tex] that satisfy [tex]\( f(x) = 18 \)[/tex] are [tex]\( x = 6 \)[/tex] and [tex]\( x = -2 \)[/tex].
Thus, the correct values of [tex]\( x \)[/tex] are:
[tex]\[\boxed{-2 \text{ and } 6}\][/tex]
So, the answer is:
[tex]\[ x = -2, x = 6 \][/tex]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.