need help solving this equation? ((please))?

Question

|x+1|=2x
this is an absolute value equation

Answer 1

First, do this:
Case 1: If x+1≥0 (meaning if it's non-negative, take note, it's non-negative and not POSITIVE), then x+1=2x.
This is true because of a general rule that I'd like to clarify using another example. Take |x|=2. In this equation, you could clearly state that x=2 or -2, since the absolute value of a negative number is equal to its additive inverse. So going back to our equation.

Solve for x in both equation and inequality as follows:
x+1≥0 ---> x≥ -1
x+1=2x ----> -x=-1 -----> x=1

Now get the intersection of these two, the x≥ -1 and x=1. To get the intersection, it is helpful to graph the two statements on the number line, a line with numbers as labels.
The first statement includes ALL REAL NUMBERS from -1 and above. This could be represented by a ray with a shaded point starting from -1 then going to the right in the number line.

The next statement could be represented by simply a shaded point above 1 in the number line.

So there you go. Now to get the intersection, just look at the area where both statements meet, and that is x=1.

So there you have it.
Next,
Case 2: If x+1<0 (meaning if it's negative), then -(x+1)=2x.
x+1<0 intersecting with -x-1=2x
x<-1 intersecting with -3x=1
x< -1 intersecting with x= -1/3
Since when graphed, the ray of x< -1 is pointing to the left, and x= -1/3 is on its right, there is no intersection. So the intersection is a null set denoted as Ø.

Now, you have these 2 intersections, x=1 and Ø, now get their union. To get the union, just do what to do in getting the intersection, but instead of looking at the area where they meet, look at the area that they COVER not MEET. So when graphing x=1, it's a big dot over 1 in the number line, and a null set is just, basically nothing. So, the union is x=1.

To correct way to write the answer is like this:
SS: {x|x ɛ R||x=1}

This is read as "the solution set is the set of all x's such that x is an element of the set of real numbers such that x is equal to 1."

Answer 2

x is 1

Answer 3

x=1?

Answer 4

The absolute value of x+1 is x+1, so as far as I can figure it the equation would be x+1=2x

Answer 5

Ok, let's see,

for x > = 0, we have

x+1 = 2x

x= 1 as your first solution

for x < 0

the solution does not exist because the absolute value is always postive...if cannot equate 2 times a negative number. So, the only solution is x = 1.

Good luck!

Answer 6

First, remove the absolute bars and solve regularly. Then x+1 = 2x and x=1. There is no negative x that will be a solution.

Answer 7

so, x+1 = 2x for one solution, and -(x+1) = 2x for the other.
1) subtracting x, we get: 1 = x.
2) collecting terms gives us: -x-1 = 2x
adding x gives: -1 = 3x
dividing by 3 gives -1/3 = x

so the two points are where x = 1 and -1/3.

Answer 8

(x+1)^2=2x^2
x^2+1+2x=2x^2
x^2-2x-1=0
x=[2+/-sqrt(4+4)]/2
=[2+/- 2x sqrt(2)]/2
=1+/-sqrt(2)]. ANS.

Answer 9

x+1=2x
-1 -1
_______
x=1x
____
1
x=1