Question:
\(|\frac{x}{2} - 1|<3\) implies that \(x\) lies in the interval
\(|\frac{x}{2} - 1|<3\) implies that \(x\) lies in the interval
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Always isolate the variable step by step when solving modulus inequalities.
Updated On: Apr 15, 2026
- (-4,8)
- (-3,6)
- (-4,6)
- (-3,8)
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The Correct Option is A
Solution and Explanation
Concept:
\[
|A|<k \Rightarrow -k<A<k
\]
Step 1: Apply inequality.
\[ -3<\frac{x}{2} - 1<3 \]
Step 2: Add 1.
\[ -2<\frac{x}{2}<4 \]
Step 3: Multiply by 2.
\[ -4<x<8 \]
Step 1: Apply inequality.
\[ -3<\frac{x}{2} - 1<3 \]
Step 2: Add 1.
\[ -2<\frac{x}{2}<4 \]
Step 3: Multiply by 2.
\[ -4<x<8 \]
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