Question

|2x + 3| = x + 1
can anyone explain to me why it has no solution?

Answer 1

\(|2x+3|=x+1\therefore-2x-3=x+1,2x+3=x+1\) And the solutions for \(x\) do exist, unless I'm mistaken.

Answer 2

@badreferences It appears you may be mistaken. http://www.wolframalpha.com/input/?i=abs%282x%2B3%29+%3D+x%2B1

Answer 3

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

Answer 4

It's true, I forgot to bound the values for the absolute values. My badd.

Answer 5

Perhaps, you should acquire some goodreferences? :-P

Answer 6

My name shall forevermore haunt me. XD

Answer 7

x is -2

Answer 8

remember the domain for the absolute value (refer to my post above)

Answer 9

I don't understand!

Answer 10

What a terrible mistake to make.

Answer 11

@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.

Answer 12

thx guys

Answer 13

find the value of X