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Solution of || x-1|+2| \leqslant 4  is

Option: 1

\left [ -1,3 \right ]

 

 

 


Option: 2

\left [ 1,3 \right ]


Option: 3

\left [ 4,5 \right ]


Option: 4

None of these


Answers (1)

best_answer

\begin{aligned} &\qquad|| x-1|+2| \leq 4 \Rightarrow-4 \leq|x-1|+2 \leq 4 \\ \end{aligned}

\begin{aligned} &\Rightarrow-6 \leq|x-1| \leq 2 \\ &\Rightarrow-6 \leq|x-1| \text { and }|x-1| \leq 2 \end{aligned}

As |x-1| \geqslant-6 is always true so, solution of |x-1| \geqslant-6 is R

Now

\begin{aligned} &|x-1| \leq 2 \\ \Rightarrow &-2 \leq x-1 \leq 2 \\ \Rightarrow &-1 \leq x \leq 3 . \end{aligned}

So, Solution is R \cap[-1,3]=[-1,3]

Posted by

Gunjita

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