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 February 17th, 2018, 08:11 PM #11 Global Moderator   Joined: Dec 2006 Posts: 19,958 Thanks: 1844 Squaring gives $x^2 + 4x + 4 = x^2 + 14x + 49$, i.e. $10x + 45 = 0$, so $x = -9/2$. Why would that be wanted as an interval? Was the question mistyped?
February 17th, 2018, 08:19 PM   #12
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 Originally Posted by skeeter No thanks. Went in January ... an expensive lesson in “hurry up & wait”
Sounds like somebody got their FastPass selections wrong.

February 19th, 2018, 11:26 AM   #13
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 Originally Posted by shaharhada It's not my equation, but I want to understand the solution in the beginning part: but seriously folks... $|x+2| = |x+7|$ you can split this into 3 areas *$x < -7$ *$-7 \leq x \leq -2$ *$-2 < x$ In what way you get the (*) inequation?
It's derived from the definition of "absolute value". |x|= -x if x is negative, and |x|= x if x is non-negative. If x+ 7 is negative (so x< -7) |x+ 7|= -(x+7). If x+7 is non-negative (so $x\ge -7$) |x+7|= |x+7|. If x+ 2 is negative (so x< -2) |x+ 2|=-(x+ 2). If x+ 2 is non-negative (so $x\le -2$) |x+ 2|= x+ 2.

That's why romsek divided this into three regions, $x< -7$, $-7\le x< -2$, and $-2\le x$. In the first region x is less than both -7 and -2, in the second, x is larger than -7 but still less than -2, and in the third, x is greater than both -7 and -2.

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