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  • Solve for x the inequalities in |x-1|<5, |x|>2

Solve for x, the inequalities in \left | x -1 \right |\leq 5,\left | x \right |\geq 2    

Answers (1)

\left | x-1 \right |\leq 5........(given)

(i) Now, there will be two cases –

x-1 \leq 5,

Adding 1 on both the sides, we get,

x \leq 6

(ii) -\left (x-1 \right ) \leq 5

i.e., -x+1 \leq 5

Subtract 1 from both the sides, we will get,

-x \leq 4 i.e x \geq -4

Now, from (i) & (ii), we get,           

-4 \leq x\leq 6.........(a)

& \left | x \right |\geq 2'

Thus, x \geq 2 & -x \geq 2

Thus x \leq -2

i.e x \epsilon( -4,-2] \cup [ 2,6] 

Posted by

infoexpert22

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