Question
\( |x-2|=9 \) \( x=\square \) (smaller value) \( x=\square \) (larger value)
Ask by Spencer Watson. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -7 \) and \( x = 11 \).
Solution
To solve the equation \( |x - 2| = 9 \), we consider the definition of absolute value, which leads to two possible scenarios:
1. **Positive Case:**
\[
x - 2 = 9 \\
x = 9 + 2 \\
x = 11
\]
2. **Negative Case:**
\[
x - 2 = -9 \\
x = -9 + 2 \\
x = -7
\]
Therefore, the solutions are:
\[
x = -7 \quad \text{(smaller value)}
\]
\[
x = 11 \quad \text{(larger value)}
\]
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Simplify this solution Extra Insights
To solve the equation \( |x-2|=9 \), we need to consider the definition of absolute value. This leads us to two possible equations: 1. \( x - 2 = 9 \) which simplifies to \( x = 11 \) (the larger value). 2. \( x - 2 = -9 \) which simplifies to \( x = -7 \) (the smaller value). Thus, we have \( x=-7 \) (smaller value) and \( x=11 \) (larger value). So, \( x=\square \) (smaller value) is \(-7\) and \( x=\square \) (larger value) is \(11\).
