How do you solve # |x - 2| + 10 = 12#?

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Answer 1 · 2016-06-30T18:45:29

The Solns. are #x=0,x=4#

#|x-2|+10=12 rArr |x-2|=12-10=2...............(1)#

Recall that, #|y|=+-y#

Hence, by #(1), +-(x-2)=2#

Case (1)
#+(x-2)=2 rArr x=4.#

Case (2)
#-(x-2)=2 rArr x-2=-2 rArr x=2-2=0.#

These satisfy the eqn.

Hence, the Solns. are #x=0,x=4#