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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,∞)