(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

i) x^3 + x^2 > 2x

ii) l 2 - x l =< 4

(modulus of 2 - x is greater than or equal to 4)

3. 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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# Help with finding least upper bounds and greatest lower bounds?

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