Solve the following system of equations in R- -x-2-1-x-2-2- 0

|x 2| 1/|x 2| 2≤ 0 Let y=|x 2| ⇒y 1/y 2≤ 0 ⇒ 1≤ y lt;2 ⇒ 1≤ |x 2| lt;2 ⇒ x ϵ [ 2+2, 1+2]∪ [1+2,2+2] ⇒ xϵ [0,1]∪ [3,4] The solution set is [0,1]∪ [3,4] ...

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Standard XII

Mathematics

Inequalities Involving Modulus Function

Solve the fol...

Question

Solve the following system of equations in R.
$\frac{| x - 2 | - 1}{| x - 2 | - 2} \leq 0$

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Solution

$\frac{| x - 2 | - 1}{| x - 2 | - 2} \leq 0 L e t y = | x - 2 | \Rightarrow \frac{y - 1}{y - 2} \leq 0 \Rightarrow 1 \leq y < 2 \Rightarrow 1 \leq | x - 2 | < 2 \Rightarrow x ϵ [- 2 + 2, - 1 + 2] \cup [1 + 2, 2 + 2] \Rightarrow x ϵ [0, 1] \cup [3, 4] T h e s o l u t i o n s e t i s [0, 1] \cup [3, 4]$

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