Solve |x+5| < 2: Absolute Value Inequality Analysis

Given:

∣x+5∣<2 |x+5| < 2

Which of the following statements is necessarily true?

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1

Understand the problem

Given:

∣x+5∣<2 |x+5| < 2

Which of the following statements is necessarily true?

2

Step-by-step solution

To solve the inequality ∣x+5∣<2 |x+5| < 2 , apply the property of absolute values which states that ∣a∣<b |a| < b translates to −b<a<b -b < a < b .

Therefore, −2<x+5<2 -2 < x+5 < 2 .

Subtract 5 from all parts of the inequality to isolate x x :

−2−5<x+5−5<2−5 -2 - 5 < x+5 - 5 < 2 - 5

This simplifies to −7<x<−3 -7 < x < -3 .

3

Final Answer

−7<x<−3 -7 < x < -3

Practice Quiz

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Given:

\( \left|2x-1\right|>-10 \)

Which of the following statements is necessarily true?

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