anonymous
  • anonymous
|2x + 3| = x + 1 can anyone explain to me why it has no solution?
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\(|2x+3|=x+1\therefore-2x-3=x+1,2x+3=x+1\) And the solutions for \(x\) do exist, unless I'm mistaken.
anonymous
  • anonymous
@badreferences It appears you may be mistaken. http://www.wolframalpha.com/input/?i=abs%282x%2B3%29+%3D+x%2B1
anonymous
  • anonymous
for values of 2x+3<0, -2x-3 = x+1 for values of 2x+3>=0, 2x+3 = x+1 So we solve for 2x+3<0 (x<-3/2) -2x-3=x+1 -4=3x x=-4/3 Solve for 2x+3>=0 (x>=-3/2) 2x+3 = x+1 x=-2 So the two solutions are (x=-4/3 and x=-2) But we have a problem... x = -4/3 is only valid for values of x<-3/2 -4/3 is greater than -3/2 so we cannot count this as a solution Same with x = -2. It is only valid for values of x>=-3/2 -2 is less than -3/2 so we cannot count this as a solution. Therefore there are no solutions

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anonymous
  • anonymous
It's true, I forgot to bound the values for the absolute values. My badd.
anonymous
  • anonymous
Perhaps, you should acquire some goodreferences? :-P
anonymous
  • anonymous
My name shall forevermore haunt me. XD
anonymous
  • anonymous
x is -2
anonymous
  • anonymous
remember the domain for the absolute value (refer to my post above)
anonymous
  • anonymous
I don't understand!
anonymous
  • anonymous
What a terrible mistake to make.
anonymous
  • anonymous
@leemichaeljh when we are solving for non-negative values of 2x+3 (the bit inside the abs), we must take into account that if 2x+3 >= 0, then x >= -3/2. After simplifying 2x+3 = x+1, we can deduce that x = -2, but this conflicts with x >= -3/2 so this is not a solution for x.
anonymous
  • anonymous
thx guys
anonymous
  • anonymous
find the value of X

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