Answer :
To find the solutions to the equation [tex]\( |x| = 49 \)[/tex], we need to understand what the absolute value means. The absolute value of a number [tex]\( x \)[/tex] is the distance of [tex]\( x \)[/tex] from 0 on the number line, and it is always non-negative. Therefore, the absolute value equation [tex]\( |x| = 49 \)[/tex] means that [tex]\( x \)[/tex] can either be 49 or -49, since both of these numbers are exactly 49 units from 0.
Now, let's examine the given options to see which ones satisfy the equation:
A. 9: The absolute value of 9 is [tex]\( |9| = 9 \)[/tex], which is not equal to 49.
B. 7: The absolute value of 7 is [tex]\( |7| = 7 \)[/tex], which is not equal to 49.
C. -7: The absolute value of -7 is [tex]\( |-7| = 7 \)[/tex], which is not equal to 49.
D. -49: The absolute value of -49 is [tex]\( |-49| = 49 \)[/tex], which matches our equation.
E. 49: The absolute value of 49 is [tex]\( |49| = 49 \)[/tex], which matches our equation.
F. None of these: This option would be incorrect because two of the numbers, -49 and 49, are indeed solutions to the equation.
Therefore, the numbers that solve the equation [tex]\( |x| = 49 \)[/tex] from the given options are D. -49 and E. 49.
Now, let's examine the given options to see which ones satisfy the equation:
A. 9: The absolute value of 9 is [tex]\( |9| = 9 \)[/tex], which is not equal to 49.
B. 7: The absolute value of 7 is [tex]\( |7| = 7 \)[/tex], which is not equal to 49.
C. -7: The absolute value of -7 is [tex]\( |-7| = 7 \)[/tex], which is not equal to 49.
D. -49: The absolute value of -49 is [tex]\( |-49| = 49 \)[/tex], which matches our equation.
E. 49: The absolute value of 49 is [tex]\( |49| = 49 \)[/tex], which matches our equation.
F. None of these: This option would be incorrect because two of the numbers, -49 and 49, are indeed solutions to the equation.
Therefore, the numbers that solve the equation [tex]\( |x| = 49 \)[/tex] from the given options are D. -49 and E. 49.
