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For which equations below is [tex]$x = -3$[/tex] a possible solution? Select three options.

A. [tex]|x| = 3[/tex]
B. [tex]|x| = -3[/tex]
C. [tex]|-x| = 3[/tex]
D. [tex]|-x| = -3[/tex]
E. [tex]-|x| = -3[/tex]

Sagot :

GinnyAnsweridn
Let's analyze each of the given equations to determine if [tex]\( x = -3 \)[/tex] is a solution.

1. Equation: [tex]\(|x| = 3\)[/tex]

To solve [tex]\(|x| = 3\)[/tex], compute the absolute value of [tex]\( x \)[/tex]:
[tex]\[ |x| = |-3| = 3 \][/tex]
Since [tex]\( 3 = 3 \)[/tex], this equation is true.

2. Equation: [tex]\(|x| = -3\)[/tex]

The absolute value of any number is always non-negative (i.e., greater than or equal to zero). Therefore, [tex]\(|x| = -3\)[/tex] doesn't make sense because [tex]\(-3\)[/tex] is negative. This equation is false.

3. Equation: [tex]\(|-x| = 3\)[/tex]

Compute the absolute value of [tex]\(-x\)[/tex] where [tex]\( x = -3 \)[/tex]:
[tex]\[ |-x| = -(-3) = |-3| = 3 \][/tex]
Since [tex]\( 3 = 3 \)[/tex], this equation is true.

4. Equation: [tex]\(|-x| = -3\)[/tex]

As previously mentioned, the absolute value must always be non-negative. Therefore, [tex]\(|-x| = -3\)[/tex] does not make sense and is false.

5. Equation: [tex]\(-|x| = -3\)[/tex]

Compute the absolute value of [tex]\( x \)[/tex] and then take the negative of it:
[tex]\[ -|x| = -|-3| = -3 \][/tex]
Since [tex]\(-3 = -3\)[/tex], this equation is true.

Based on the analysis, the three equations for which [tex]\( x = -3 \)[/tex] is a solution are:

1. [tex]\(|x| = 3\)[/tex]
2. [tex]\(|-x| = 3\)[/tex]
3. [tex]\(-|x| = -3\)[/tex]
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