Question

If |x-2| less than= 5 then x lies in the interval​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{|x-2|\,\leq\,5}$

$\underline{\textbf{To find:}}$

$\textsf{Solution set of the inequality}\;\mathsf{|x-2|\,\leq\,5}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{|x-2|\,\leq\,5}$

$\implies\mathsf{-5\,\leq\,x-2\,\leq\,5}$

$\textsf{Adding 2 through out,}$

$\mathsf{-5+2\,\leq\,x-2+2\,\leq\,5+2}$

$\mathsf{-3\,\leq\,x\,\leq\,7}$

$\implies\bf\,x\,\in\,[-3,7]$

$\underline{\textbf{Formula used:}}$

$\boxed{\begin{minipage}{6cm} \\\mathsf{If\;|x|\,\leq\,r,\;then\;-r\,\leq\,x\,\leq\,r} \end{minipage}}$

Answer 2

Answer:

X lies in the interval $\mathrm{x} \in[-3,7]$

Step-by-step explanation:

Given:

$|x-2| \leq 5$

To find:

Solution set of the inequality $|x-2| \leq 5$

Solution:

Formula used:

$\text { If }|x| \leq r \text {, then }-r \leq x \leq r$

Consider,

$|x-2| \leq 5$

$\Longrightarrow-5 \leq x-2 \leq 5$

Adding 2 through out,

$-5+2 \leq x-2+2 \leq 5+2$

$-3 \leq x \leq 7$

$\Longrightarrow \mathrm{x} \in[-3,7]$