Question

find range of x for..... ​

Answer 1

Your pic is unclear.

So please don't expect 100% right solution.

Answer 2

Answer :

x € [ - 2 , 4 ]

For solution , please refer to the attachment .

Note:

★ The modules or absolute value of a number x is denoted by |x| .

★ The modules of the number x is defined as ;

|x| = x , if x ≥ 0

= -x , if x < 0

★ The modules of the number x can also be defined as ;

|x| = max{ x , -x }

★ |x| = a => x = ±a

★ |x| < a => x € (-a , a)

★ |x| > a => x € (-∞,-a) U (a,∞)

★ |x| > 0 => x € R

★ |x| < 0 => x € ∅

★ |x| > -ve no. => x € R

★ |x| < -ve no. => x € ∅