Question

Find k' for which following equation has 4 solutions = |x - 1| - 2|x| + |2x + 1|= k

Answer 1

Answer:

|x-1|-2|x|+|2x+1|=k

x+1-2x+2x+1=k

x+1+1=k

x+2=k

k=x+2

k-x=2

therefore now let k and x be a and b

therefore a-b =2

therefore we can write it as a-(a-b)=2

a-(a-b)=2

a-a+b=2

therefore a and a been cancelled therefore now

b=2

therefore a=a-a=0and b=2

therefore k=0and x=2

Answer 2

Answer:

1<k<2 has 4 solutions

hope it useful