Solve the inequality -1 <= x^2 - 2x <= 8
Solve the inequality ` ``-1<=x^2-2x<=8 ` :
(a) `-1<=x^2-2x `
` ` `0<=(x-1)^2 `
This is true for all real values of x.
(b) `x^2-2x<=8 `
For x<-2 the left hand side is positive; try a test value like x=-3.
For -2<x<4 the left side is negative; try a test value like x=0.
For x>4 the left side is positive; try a test value like x=5.
So for `-2<=x<=4,(x-4)(x+2)<=0 `
Thus the correct solution is `-2<=x<=4 `
Here is a graph:
Excellent answer, embizze!