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 $x=0,x=4$

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