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.
