Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Sure, let's analyze each equation to determine if [tex]\(x = 9\)[/tex] is a possible solution.
1. Equation: [tex]\(|x| = 9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ |x| = |9| = 9 \][/tex]
This is true.
2. Equation: [tex]\(-|x| = 9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ -|x| = -|9| = -9 \][/tex]
This is not equal to 9. So, this is false.
3. Equation: [tex]\(-|-x| = 9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ -|-x| = -|-9| = -9 \][/tex]
This is not equal to 9. So, this is false.
4. Equation: [tex]\(-|-x| = -9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ -|-x| = -|-9| = -9 \][/tex]
This is true.
5. Equation: [tex]\(|x| = -9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ |x| = |9| = 9 \][/tex]
The absolute value cannot be negative, so this is false.
6. Equation: [tex]\(|-x| = 9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ |-x| = |-9| = 9 \][/tex]
This is true.
7. Equation: [tex]\(|-x| = -9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ |-x| = |-9| = 9 \][/tex]
Again, the absolute value cannot be negative, so this is false.
Therefore, [tex]\(x = 9\)[/tex] is a possible solution for the following equations:
1. [tex]\( |x| = 9 \)[/tex]
2. [tex]\( -|-x| = -9 \)[/tex]
3. [tex]\( |-x| = 9 \)[/tex]
1. Equation: [tex]\(|x| = 9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ |x| = |9| = 9 \][/tex]
This is true.
2. Equation: [tex]\(-|x| = 9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ -|x| = -|9| = -9 \][/tex]
This is not equal to 9. So, this is false.
3. Equation: [tex]\(-|-x| = 9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ -|-x| = -|-9| = -9 \][/tex]
This is not equal to 9. So, this is false.
4. Equation: [tex]\(-|-x| = -9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ -|-x| = -|-9| = -9 \][/tex]
This is true.
5. Equation: [tex]\(|x| = -9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ |x| = |9| = 9 \][/tex]
The absolute value cannot be negative, so this is false.
6. Equation: [tex]\(|-x| = 9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ |-x| = |-9| = 9 \][/tex]
This is true.
7. Equation: [tex]\(|-x| = -9\)[/tex]
For [tex]\(x = 9\)[/tex]:
[tex]\[ |-x| = |-9| = 9 \][/tex]
Again, the absolute value cannot be negative, so this is false.
Therefore, [tex]\(x = 9\)[/tex] is a possible solution for the following equations:
1. [tex]\( |x| = 9 \)[/tex]
2. [tex]\( -|-x| = -9 \)[/tex]
3. [tex]\( |-x| = 9 \)[/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.