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Answer :
To solve the equation [tex]\( |x| = 13 \)[/tex], we need to understand what absolute value means. The absolute value of a number [tex]\( x \)[/tex], denoted as [tex]\( |x| \)[/tex], represents the distance of [tex]\( x \)[/tex] from zero on a number line, regardless of direction. Therefore, absolute value turns negative numbers into their positive counterparts and leaves positive numbers unchanged.
Given the equation [tex]\( |x| = 13 \)[/tex], we are looking for numbers that are exactly 13 units from zero on the number line. This scenario gives us two possible solutions:
1. [tex]\( x \)[/tex] can be positive 13, because [tex]\( |13| = 13 \)[/tex].
2. [tex]\( x \)[/tex] can also be negative 13, because [tex]\( |-13| = 13 \)[/tex].
Now, let's match these solutions with the provided options:
- Option A: 1 - This is not a solution because [tex]\( |1| = 1 \)[/tex], which is not equal to 13.
- Option B: 169 - This is not a solution because [tex]\( |169| = 169 \)[/tex], which is not equal to 13.
- Option C: 13 - This is a solution because [tex]\( |13| = 13 \)[/tex].
- Option D: -13 - This is a solution because [tex]\( |-13| = 13 \)[/tex].
- Option E: -169 - This is not a solution because [tex]\( |-169| = 169 \)[/tex], which is not equal to 13.
- Option F: None - This is incorrect because there are solutions to the equation.
Based on this analysis, the correct solutions to the equation [tex]\( |x| = 13 \)[/tex] are options C and D, which are 13 and -13, respectively.
Given the equation [tex]\( |x| = 13 \)[/tex], we are looking for numbers that are exactly 13 units from zero on the number line. This scenario gives us two possible solutions:
1. [tex]\( x \)[/tex] can be positive 13, because [tex]\( |13| = 13 \)[/tex].
2. [tex]\( x \)[/tex] can also be negative 13, because [tex]\( |-13| = 13 \)[/tex].
Now, let's match these solutions with the provided options:
- Option A: 1 - This is not a solution because [tex]\( |1| = 1 \)[/tex], which is not equal to 13.
- Option B: 169 - This is not a solution because [tex]\( |169| = 169 \)[/tex], which is not equal to 13.
- Option C: 13 - This is a solution because [tex]\( |13| = 13 \)[/tex].
- Option D: -13 - This is a solution because [tex]\( |-13| = 13 \)[/tex].
- Option E: -169 - This is not a solution because [tex]\( |-169| = 169 \)[/tex], which is not equal to 13.
- Option F: None - This is incorrect because there are solutions to the equation.
Based on this analysis, the correct solutions to the equation [tex]\( |x| = 13 \)[/tex] are options C and D, which are 13 and -13, respectively.
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