Solve the following system of equations in R.
|4-x|+1<3

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Solution

We have,

|4-x|+1-3<0

$\Rightarrow | 4 - x | - 2 < 0 . . . (i) C a s e I : W h e n | 4 - x | \geq 0 | 4 - x | - 2 < 0 \Rightarrow 4 - x - 2 < 0 \Rightarrow 2 - x < 0 \Rightarrow - x < - 2 \Rightarrow x > 2 . . . (i i) C a s e I I : W h e n | 4 - x | < 0 | 4 - x | - 2 < 0 \Rightarrow - (4 - x) - 2 < 0 \Rightarrow - 4 + x - 2 < 0 \Rightarrow x - 6 < 0 \Rightarrow x < 6 . . . (i i i) Combining (ii) and (iii) we get (2,6) as the solution set.$

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