Transcript Problem Presentation - Muskingum University

Problem Presentation
Meng Li
09-28-2012
Problem set 4 #5
Solve
for x:
︱x+1︱-︱x︱+2︱x-1︱=2x-1
Solution
Solve
for x:
︱x+1︱-︱x︱+2︱x-1︱=2x-1
The
first step to solve the equation is taking
the sign of the absolute value off.
SOLUTION
 HINT:
│X│= -X; X<0
│X│= 0; X=0
│X│= X; X>0
 In
order to take the sign of absolute
value off, we need to figure out the
domain of x.
SOLUTION
 Since｜0｜=
0, with which the function will
not be changed when take the sign of
absolute value off. Now we need to find
the values of X when the absolute values
equal to 0.
SOLUTION
 ∵︱x+1︱-︱x︱+2︱x-1︱=2x-1
X+1=0; X=-1

X=0; X=0

X-1=0; X=1
 Number line:
∴
We can get the number line
DOMAIN
OF x
x+1
x
x-1
FINAL EQUATION OF
︱x+1︱-︱x︱+2︱x-1 ︱=2x-1
X < -1
-
-
-
-(X+1)-(-X)+2[-(X-1)]=2X-1
2=4X
X = -1
0
-1
-2
0-1+4≠-3
-1<X<0
+
-
-
X+1-(-X)+2[-(X-1)]=2X-1
4=2X
X=0
1
0
-1
1-0+2=3≠-1
VALUE OF
X
0 <X<1
+
+
-
X+1-X+2[-(X-1)]=2X-1
4=4X
X=1
2
1
0
2-1+0=1
1
+
X+1-X+2(X-1)=2X-1
2X-1=2X-1
ANY NUMBER
GREATER THAN 1
1<X
+
+
SOLUTION
 According
to the form above, we can
find the value of X: [1,∞)