RPS #004 - Absolception

Algebra Level 4

Find sum of all real solution of $x$ which satisfies $||||x+2|+0|+1|+5| = 2015$

1 solution

Rimba Erlangga
Jan 23, 2015

if $|x| = k$ then $x = k$ or $x = -k$

then $||||x+2|+0|+1|+5 = 2015$ or $-2015$

implies that $||||x+2|+0|+1| = 2010$ or $-2020$

but since $|x|$ never be negative, so apply this until you get $|x+2| = 2009$

then $x + 2 = 2009$ or $x + 2 = -2009$

we got that $x = 2007$ or $x = -2011$ add those and the answer is $-4$