Solution of |x - 1| ? |x - 3| is

Question

Solution of $| x - 1 |$ $\geq$ $| x - 3 |$ is

Smart Achievers · Accepted Answer

(2)

$We have,$ $| x - 1 |$ $-$ $| x - 3 |$ $\geq 0$

$Also,$ $| x - 1 |$ $-$ $| x - 3 |$ $=$ ${\begin{matrix} - 2, & if x < 1 \\ 2 x - 4, & if 1 \leq x \leq 3 \\ 2, & if x > 3 \end{matrix}$

$If x < 1 \Rightarrow - 2 \geq 0, not possible$

$If 1 \leq x \leq 3$

$\Rightarrow 2 x - 4 \geq 0 \Rightarrow x \geq 2 \Rightarrow x \in [2, \infty) \Rightarrow x \in [2, 3]$

$If x > 3$

$\Rightarrow 2 \geq 0 \Rightarrow x \in (3, \infty)$

$Combining above, we get$ $x \in [2, \infty)$

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