Answer :
To solve the equation [tex]\( |x| = 49 \)[/tex], we need to understand what absolute value means. The absolute value of a number [tex]\( x \)[/tex], written as [tex]\( |x| \)[/tex], is the distance of [tex]\( x \)[/tex] from zero on the number line, without considering which direction. Therefore, the absolute value is always non-negative.
For the equation [tex]\( |x| = 49 \)[/tex], we are looking for numbers [tex]\( x \)[/tex] whose distance from zero is 49. These numbers can be both positive and negative. Specifically, the solutions to [tex]\( |x| = 49 \)[/tex] are:
1. [tex]\( x = 49 \)[/tex], because the absolute value of 49 is 49.
2. [tex]\( x = -49 \)[/tex], because the absolute value of -49 is also 49.
Now, let's check each option provided to determine which numbers are solutions:
A. 9: The absolute value of 9 is 9. This is not 49, so 9 is not a solution.
B. 7: The absolute value of 7 is 7. This is not 49, so 7 is not a solution.
C. -7: The absolute value of -7 is 7. This is not 49, so -7 is not a solution.
D. -49: The absolute value of -49 is 49. This matches the equation, so -49 is a solution.
E. 49: The absolute value of 49 is 49. This matches the equation, so 49 is a solution.
F. None of these: Since we found solutions among the given options, this choice is not applicable.
Therefore, the numbers that are solutions to the equation [tex]\( |x| = 49 \)[/tex] are [tex]\(-49\)[/tex] and [tex]\(49\)[/tex].
For the equation [tex]\( |x| = 49 \)[/tex], we are looking for numbers [tex]\( x \)[/tex] whose distance from zero is 49. These numbers can be both positive and negative. Specifically, the solutions to [tex]\( |x| = 49 \)[/tex] are:
1. [tex]\( x = 49 \)[/tex], because the absolute value of 49 is 49.
2. [tex]\( x = -49 \)[/tex], because the absolute value of -49 is also 49.
Now, let's check each option provided to determine which numbers are solutions:
A. 9: The absolute value of 9 is 9. This is not 49, so 9 is not a solution.
B. 7: The absolute value of 7 is 7. This is not 49, so 7 is not a solution.
C. -7: The absolute value of -7 is 7. This is not 49, so -7 is not a solution.
D. -49: The absolute value of -49 is 49. This matches the equation, so -49 is a solution.
E. 49: The absolute value of 49 is 49. This matches the equation, so 49 is a solution.
F. None of these: Since we found solutions among the given options, this choice is not applicable.
Therefore, the numbers that are solutions to the equation [tex]\( |x| = 49 \)[/tex] are [tex]\(-49\)[/tex] and [tex]\(49\)[/tex].
