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Modulus Function

Solve for x...

Question

Solve for $x$ = $| x - 1 | + | x - 2 | \leq 3$

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Solution

$| x - 1 | + | x - 2 | \leq 3 N o d a l p o i n t s a r e 1, 2. w h e n x < 1 - (x - 1) - (x - 2) \leq 3 - x + 1 - x + 2 \leq 3 - 2 x + 3 \leq 3 - 2 x \leq 0 x \geq 0 - (i) w h e n 1 \leq x < 2 (x - 1) - (x - 2) \leq 3 x - 1 - x + 2 \leq 3 x \leq 3 x ϵ R - (i i) w h e n x \geq 2 x - 1 + x - 2 \leq 3 2 x - 3 \leq 3 2 x \leq 6 x \leq 3 - (i i i) f r o m (i), (i i) & (i i i) x ϵ [0, 3]$

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