Answer :
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
