First slide

Operations on Sets

Question

$Set of all values of x satisfying the equation | x + 1 | = 5 - | x - 4 | is$

Moderate

A

$[- 1, 4]$
B

$(- \infty, - 1] \cup [4, \infty)$
C

$[- 1, 6]$
D

$[0, 10]$

Solution

$\begin{array}{l} | x + 1 | = 5 - | x - 4 | \\ \Rightarrow | x + 1 | + | x - 4 | = 5 \\ \Rightarrow | x + 1 | + | x - 4 | = | (x + 1) + (4 - x) | (\sin c e |x + y| = |x| + |y| h a p p e n s i f b o t h x a n d y a r e p o s i t i v e o r n e g a t i v e i . e x y \geq 0) \\ \Rightarrow (x + 1) (4 - x) \geq 0 \\ \Rightarrow (x + 1) (x - 4) \leq 0 \\ \Rightarrow x \in [- 1, 4] \end{array}$

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