Answer :
To solve the equation [tex]\( |x| = 13 \)[/tex], we need to understand what the absolute value symbol [tex]\( | \cdot | \)[/tex] means.
The absolute value of a number is its distance from 0 on the number line, without considering direction. Therefore, when you have the equation [tex]\( |x| = 13 \)[/tex], it means that [tex]\( x \)[/tex] is 13 units away from 0. This can happen in two scenarios:
1. [tex]\( x \)[/tex] is exactly 13 units to the right of 0, which means [tex]\( x = 13 \)[/tex].
2. [tex]\( x \)[/tex] is exactly 13 units to the left of 0, which means [tex]\( x = -13 \)[/tex].
So, the two solutions to the equation [tex]\( |x| = 13 \)[/tex] are [tex]\( x = 13 \)[/tex] and [tex]\( x = -13 \)[/tex].
Now, let's check the options provided:
A. 1 - This is not a solution because 1 is not 13 units away from 0.
B. 169 - This is not a solution because 169 is not the absolute value of 13.
C. 13 - Yes! This is a solution because [tex]\( x = 13 \)[/tex].
D. -13 - Yes! This is also a solution because [tex]\( x = -13 \)[/tex].
E. -169 - This is not a solution because -169 is not the absolute value of 13.
F. None - This is incorrect because there are solutions.
Therefore, the correct solutions in the options given are:
- C. 13
- D. -13
The absolute value of a number is its distance from 0 on the number line, without considering direction. Therefore, when you have the equation [tex]\( |x| = 13 \)[/tex], it means that [tex]\( x \)[/tex] is 13 units away from 0. This can happen in two scenarios:
1. [tex]\( x \)[/tex] is exactly 13 units to the right of 0, which means [tex]\( x = 13 \)[/tex].
2. [tex]\( x \)[/tex] is exactly 13 units to the left of 0, which means [tex]\( x = -13 \)[/tex].
So, the two solutions to the equation [tex]\( |x| = 13 \)[/tex] are [tex]\( x = 13 \)[/tex] and [tex]\( x = -13 \)[/tex].
Now, let's check the options provided:
A. 1 - This is not a solution because 1 is not 13 units away from 0.
B. 169 - This is not a solution because 169 is not the absolute value of 13.
C. 13 - Yes! This is a solution because [tex]\( x = 13 \)[/tex].
D. -13 - Yes! This is also a solution because [tex]\( x = -13 \)[/tex].
E. -169 - This is not a solution because -169 is not the absolute value of 13.
F. None - This is incorrect because there are solutions.
Therefore, the correct solutions in the options given are:
- C. 13
- D. -13
