# Write the Solution Set of the Equation |2 − X| = X − 2. - Mathematics

Write the solution set of the equation |2 − x| = x − 2.

#### Solution

$\text{ We have },$
$\left| 2 - x \right| = x - 2$
$\text{ Now 2 cases arise } .$
$\text{ CASE 1: When 2 } - x \geq 0, \text{ then } \left| 2 - x \right| = 2 - x$
$\Rightarrow \left| 2 - x \right| = x - 2$
$\Rightarrow 2 - x = x - 2$
$\Rightarrow 2x = 4$
$\Rightarrow x = 2$
$\text{ So, this condition is satisfied when } x = 2 .$
$\text{ CASE 2: When } 2 - x < 0 \left( \text{ i . e . when } x > 2 \right), \text{ then } \left| 2 - x \right| = - (2 - x)$
$\Rightarrow \left| 2 - x \right| = x - 2$
$\Rightarrow - (2 - x) = x - 2$
$\Rightarrow - 2 + x = x - 2$
$\Rightarrow - 2 = - 2$
$\text{ So, this condition is satisfied when } x > 2$
$\text{ Hence, from the given two cases, the solution set of the given equation is } [2, \infty )$


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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Q 4 | Page 31