Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To solve the equation [tex]\( 9|x-1| = -45 \)[/tex], let's proceed with a step-by-step analysis.
1. Simplify the equation:
- First, we want to isolate the absolute value. We can do this by dividing both sides of the equation by 9:
[tex]\[ 9|x-1| = -45 \][/tex]
Dividing both sides by 9:
[tex]\[ |x-1| = \frac{-45}{9} \][/tex]
[tex]\[ |x-1| = -5 \][/tex]
2. Analyze the absolute value:
- The equation now is [tex]\( |x-1| = -5 \)[/tex].
- The absolute value [tex]\( |x-1| \)[/tex] represents the distance between [tex]\( x \)[/tex] and 1 on the number line, and by definition, an absolute value cannot be negative. Therefore, [tex]\( |x-1| = -5 \)[/tex] is not possible because the result of an absolute value cannot be negative.
3. Conclusion:
- Since [tex]\( |x-1| = -5 \)[/tex] has no valid solutions and is not possible, there are no values of [tex]\( x \)[/tex] that satisfy the original equation [tex]\( 9|x-1| = -45 \)[/tex].
Thus, the solution to the equation [tex]\( 9|x-1| = -45 \)[/tex] is:
B. No Solution
1. Simplify the equation:
- First, we want to isolate the absolute value. We can do this by dividing both sides of the equation by 9:
[tex]\[ 9|x-1| = -45 \][/tex]
Dividing both sides by 9:
[tex]\[ |x-1| = \frac{-45}{9} \][/tex]
[tex]\[ |x-1| = -5 \][/tex]
2. Analyze the absolute value:
- The equation now is [tex]\( |x-1| = -5 \)[/tex].
- The absolute value [tex]\( |x-1| \)[/tex] represents the distance between [tex]\( x \)[/tex] and 1 on the number line, and by definition, an absolute value cannot be negative. Therefore, [tex]\( |x-1| = -5 \)[/tex] is not possible because the result of an absolute value cannot be negative.
3. Conclusion:
- Since [tex]\( |x-1| = -5 \)[/tex] has no valid solutions and is not possible, there are no values of [tex]\( x \)[/tex] that satisfy the original equation [tex]\( 9|x-1| = -45 \)[/tex].
Thus, the solution to the equation [tex]\( 9|x-1| = -45 \)[/tex] is:
B. No Solution
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.