If |x-1| - |x| + |2x+3| $>$ 2x + 4 then ?

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Solution

The correct option is A

Again use the technique of going from answer options. We need to find the range of x for which LHS $>$ RHS
Choose a value for x which is there is 2 answer options and not there in 2 answer options.
Take x = 2
LHS = |x-1| - |x| + |2x+3| = 1-2+7 = 6
RHS = 2x + 4 = 8
LHS $<$ RHS.
Hence, option (b) and (c) can be ruled out.
Next put x = $\frac{1}{2}$ .
LHS = $\frac{1}{2} - \frac{1}{2} + 4 = 4$
RHS = 1 + 4 = 5
LHS $<$ RHS. Hence, option (d) is ruled out. Answer is option (a)

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