solve and write interval notation

Question

Solve  (x^2-9) ≤0  and write interval notation for the solution set. Show careful algebraic work/explanation.

             x

Answer 1

For x²-9=(x+3)(x-3)≤0 x+3 and x-3 must be of opposite sign.

x+3≥0 and x-3≤0 for x≥-3 and x≤3 That is -3≤x≤3

The other condition that x+3≤0 and x-3≥0 is impossible.

Answer 2

Just to add to that, (# means a left bound but not inclusive of # while [# means a left bound inclusive of the #

 

#) means a non-inclusive right bound while #] means inclusive right bound

 

by convention--although it makes sense if you think about it-- if infinity is our "upper bound", we always write it as ∞) and likewise if negative infinity is our lower bound we write (-∞

 

we do not use ] or [ with infinity ....infinity is more of a concept, not a specific attainable number, intuitively speaking

 

for instance, if we wanted to describe all numbers between 2 (inclusive) and infinity, we write [2, infinity)

 

or all reals numbers we write (-inf, +inf)

 

 

in any event, the above solution as described by Michael, in interval notation is [-3,3]