# Mark the correct alternative in each of the following: If | x + 2 | ≤ 9, then - Mathematics

MCQ

Mark the correct alternative in each of the following:
If $\left| x + 2 \right|$$\leq$9, then

#### Options

• (a) x$\in$($-$7, 11)

• (b) x$\in$[$-$11, 7]

• (c) x$\in$($-$$\infty$$-$7) $\cup$(11, $\infty$)

• (d) x$\in$($-$$\infty$$-$7) $\cup$[11,$\infty$

#### Solution

$\left| x + 2 \right| \leq 9$
$\Rightarrow - 9 \leq x + 2 \leq 9$
$\Rightarrow - 9 - 2 \leq x + 2 - 2 \leq 9 - 2$
$\Rightarrow - 11 \leq x \leq 7$
$\Rightarrow x \in \left[ - 11, 7 \right]$

Hence, the correct option is (b).

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Q 7 | Page 32