Answer :
To determine which numbers are solutions to the equation [tex]\(|x| = 49\)[/tex], let's go step-by-step to understand what this equation represents.
1. Understanding the Absolute Value Equation:
- The equation [tex]\(|x| = 49\)[/tex] means we are looking for numbers [tex]\(x\)[/tex] whose absolute value is 49.
- Absolute value [tex]\(|x|\)[/tex] represents the distance of [tex]\(x\)[/tex] from zero on the number line, without considering direction. Therefore, [tex]\(|x| = 49\)[/tex] means [tex]\(x\)[/tex] can be either 49 or -49, as both of these numbers are 49 units away from zero.
2. Analyzing Each Option:
- A. 9: The absolute value of 9 is 9, which is not equal to 49.
- B. 7: The absolute value of 7 is 7, which is not equal to 49.
- C. -7: The absolute value of -7 is 7, which is not equal to 49.
- D. -49: The absolute value of -49 is 49, which satisfies the equation.
- E. 49: The absolute value of 49 is 49, which satisfies the equation.
- F. None of these: This is incorrect because options D and E are true solutions to the equation.
3. Conclusion:
- After examining all the options, the numbers -49 and 49 are both solutions to the equation [tex]\(|x| = 49\)[/tex].
Therefore, the correct answers are D (-49) and E (49).
1. Understanding the Absolute Value Equation:
- The equation [tex]\(|x| = 49\)[/tex] means we are looking for numbers [tex]\(x\)[/tex] whose absolute value is 49.
- Absolute value [tex]\(|x|\)[/tex] represents the distance of [tex]\(x\)[/tex] from zero on the number line, without considering direction. Therefore, [tex]\(|x| = 49\)[/tex] means [tex]\(x\)[/tex] can be either 49 or -49, as both of these numbers are 49 units away from zero.
2. Analyzing Each Option:
- A. 9: The absolute value of 9 is 9, which is not equal to 49.
- B. 7: The absolute value of 7 is 7, which is not equal to 49.
- C. -7: The absolute value of -7 is 7, which is not equal to 49.
- D. -49: The absolute value of -49 is 49, which satisfies the equation.
- E. 49: The absolute value of 49 is 49, which satisfies the equation.
- F. None of these: This is incorrect because options D and E are true solutions to the equation.
3. Conclusion:
- After examining all the options, the numbers -49 and 49 are both solutions to the equation [tex]\(|x| = 49\)[/tex].
Therefore, the correct answers are D (-49) and E (49).
