Express the values of x that satisfy the inequality -3 ≤ x < 7 as an interval.
Find all values of s (s + 4)(s - 3) ≤ 0such that . Give your answer as an interval.
Find all values of x that satisfy x(x+7.5) > 38.5. Give your answer in interval notation.
Find all values of t such that 8t^2 ≤ 3-10t.
Find all values of z such that {3-z}/{z+1} ≥ 1. Answer in interval notation.
For how many integers b does the inequality z^2 + bz + 15 < 0 have no real solutions z?
Find all values of c such that c^3 + 4c > 5c^2. Answer with interval notation.
+129839 Express the values of x that satisfy the inequality -3 ≤ x < 7 as an interval.
[-3, 7)
Find all values of s (s + 4)(s - 3) ≤ 0 Give your answer as an interval.
Let's solve this
s(s + 4)(s -3) = 0 the three solutions are s =0, s = -4 and s = 3
Then, the solutions to this inequality will occur on one or more of these possible intervals (-infinity, -4] , [-4, 0], [0,3] or [3, ifinity)
The intervals (-infinity, -4] and [0, 3] will satify the inequality.....here's a graph : 
+129839 Find all values of x that satisfy x(x+7.5) > 38.5. Give your answer in interval notation.
Let's solve this : x(x + 7.5) = 38.5 subtract 88.5 from both sides and simplify
x^2 + 7.5x - 38.5 = 0 factor as
(x - 3.5) ( x + 11) = 0 the solutions will come from one or more of these intervals :
(-infinity, -11) , (-11, 3.5) or (3.5, infinity)
The interval containing x = 0 will not satisfy the inequality which means that the intervals (-infinity, -11) and (3.5 , infinity) will make the inequality true
Here's the graph : https://www.desmos.com/calculator/ojmbgewyuz
+129839 For how many integers b does the inequality z^2 + bz + 15 < 0 have no real solutions z?
This will have no integer solutions when :
l b^2 l - 4(1)(15) < 0 simplify
l b^2 l - 60 < 0
l b^2 l < 60
And this will be true for all integer values on the interval [-7, 7].........so......the inequality will have no solutions when b is an integer from -7 to 7, inclusive
Find all values of c such that c^3 + 4c > 5c^2. Answer with interval notation.
c3-5c2+4c>0
c(c-1)(c-4)>0
possible intervals are:\((-\infty, 0), (0, 1), (1, 4), (4, \infty)\)
Test: -1
-1(-2)(-5)<0
Test: ½
(.5-1)(.5-4)/2=-.5(-3.5)/2=(7/2)/2=7/4>0
Test: 2
2(1)(-2)<0
Test: 5
5(4)(1)>0
intervals are: \((0, 1), (4, \infty)\)
