For the inequality $|x+3|≤5$ which of

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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Numbers, Quantification and Numerical Applications

Question:

For the inequality $|x+3|≤5$ which of the following is/are true :

A. x ≥ 2

B. x ≤ -8

C. $x \in [-8, 2]$

D. x= 0

E. x= 4

Choose the corret answer from the options given below :

Options:

A and B only

C and E only

C and D only

B and D only

Correct Answer:

C and D only

Explanation:

The correct answer is Option (3) → C and D only

$|x+3|≤5$

Case 1:

$x≥-3$

$x+3≤5$

$x≤2$

Case 2:

$x≤-3$

$-x-3≤5$

$-x≤8$

$x≥-8$

$∴x∈[-8, 2]$ and $x=0$