|2x + 3| = x + 1
can anyone explain to me why it has no solution?
Stacey Warren - Expert brainly.com
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\(|2x+3|=x+1\therefore-2x-3=x+1,2x+3=x+1\) And the solutions for \(x\) do exist, unless I'm mistaken.
@badreferences It appears you may be mistaken. http://www.wolframalpha.com/input/?i=abs%282x%2B3%29+%3D+x%2B1
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)
Solve for 2x+3>=0 (x>=-3/2)
2x+3 = x+1
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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It's true, I forgot to bound the values for the absolute values. My badd.
Perhaps, you should acquire some goodreferences? :-P
My name shall forevermore haunt me. XD
x is -2
remember the domain for the absolute value (refer to my post above)
I don't understand!
What a terrible mistake to make.
@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.