Set-builder notation? Need it fast! Most understandable answer will get best answer!?

Question

Ok here is the problem:

Solve for t, graph and state the solution in set-builder notation.

t(squared) + 5t - 6 (is greater than or equal to) 0

How do I do this problem? Thank you very much!!

Answer 1

t² + 5t - 6 ≥ 0

First, we factor the polynomial:

(t+6)(t-1) ≥ 0

Now, when will this be true? Clearly, if t≥1, then t+6 is positive and t-1 is nonnegative, so their product will be nonnegative. If t≤-6, then t-1 is negative, and t+6 is nonpositive, so their product will be nonnegative. However, if neither of the above is true, then -6
(t+6)(t-1) ≥ 0 ⇔ (t≤-6 ∨ t≥1)

Thus the set of t that make this true is precisely:

{t: t≤-6 ∨ t≥1}

To graph this set on the real line, place a closed dot at -6 and fill in the ray to the left of -6 (this is t≤-6), and then place a closed dot at 1 and fill in the ray to the right of 1 (this is t≥1).

Answer 2

yet what's the question? I guess you want to resolve the inequality for x. it is to assert, you want to renowned for what values of x is the inequality genuine. If I have been your instructor, i could provide you some credit in case you in basic terms positioned that inequality in brackets: { x | 5/4(x-a million/2) -5/3 < 4/3 } That answer could be technically suitable, yet i could in basic terms provide you finished credit in case you have been to re-set up the inequality in accordance to the regulations of algebra so as to isolate the variable, x.

Answer 3

(t -1)(t + 6)=(greater than or equal to) 0
t=(greater than or equal to)1
t=(greater than or equal to)-6