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The equation [tex]\(|v-2|=-5\)[/tex] has no real solution because the absolute value of any real number is always non-negative, and hence cannot be equal to -5.

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GinnyAnswer
To solve the equation [tex]\( |v-2| = -5 \)[/tex], we need to understand the properties of absolute values. Let’s break down the steps:

1. Understanding Absolute Value: The absolute value of a number represents its distance from zero on the number line, regardless of direction. This means it is always non-negative. For any real number [tex]\( x \)[/tex], [tex]\( |x| \geq 0 \)[/tex].

2. Analyzing the Given Equation:

The equation given is [tex]\( |v-2| = -5 \)[/tex]. According to the properties of absolute value, an absolute value can never be negative.

3. Considering the Validity:

Since [tex]\( |v-2| \)[/tex] represents the absolute value of [tex]\( v-2 \)[/tex], it cannot equal -5 because -5 is a negative number.

4. Conclusion:

Because it is impossible for the absolute value of any number to be negative, the given equation [tex]\( |v-2| = -5 \)[/tex] has no solution.

Thus, the final conclusion is that the equation [tex]\( |v-2| = -5 \)[/tex] has no solution.
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