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February 17th, 2018, 07:11 PM   #11
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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?
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February 17th, 2018, 07:19 PM   #12
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Originally Posted by skeeter View Post
No thanks. Went in January ... an expensive lesson in “hurry up & wait”
Sounds like somebody got their FastPass selections wrong.
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February 19th, 2018, 10:26 AM   #13
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Originally Posted by shaharhada View Post
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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