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For which equations is [tex]\( x=9 \)[/tex] a possible solution? Check all that apply.

A. [tex]\( |x|=9 \)[/tex]

B. [tex]\( -|x|=9 \)[/tex]

C. [tex]\( -|-x|=9 \)[/tex]

D. [tex]\( -|-x|=-9 \)[/tex]

E. [tex]\( |x|=-9 \)[/tex]

F. [tex]\( |-x|=9 \)[/tex]

G. [tex]\( |-x|=-9 \)[/tex]



Answer :

GinnyAnswer
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]

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