- #1
mgnymph
- 15
- 0
Homework Statement
Solve the following inequalities and express the solution(s) in interval notation and set builder notation. For each of these, state the least upper bound and greatest lower bounds, if these exist.
Homework Equations
i) x^3 + x^2 > 2x
ii) l 2 - x l =< 4
(modulus of 2 - x is greater than or equal to 4)
The Attempt at a Solution
So for (i), I factorised so
x^3 + x^2 - 2x > 0
x(x^2 + x -2) > 0
x(x+2)(x-1) > 0
I am really unsure what interval notation and set builder notation are, but I think...
Interval notation: x E (-2,0) U (1 , infinity)
Set builder notation: {x : -2 < x < 0 or x > 1}
And I don't know how to find the bounds...
(ii) l 2 - x l =< 4
-4 =< 2 - x =< 4
-6 =< x =< 2
interval notation: x E [-2,6]
set builder notation: {x: -2 =< x =< 6}
and... i don't know how to find the least upper bounds/greatest lower bounds for this either.
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