x^2+3x<28 subtract 28 from each side
x^2 + 3x - 28 < 0 factor
(x + 7) (x - 4) < 0
Our answers will come from either these two invervals {- ∞, -7) and (4, ∞ )
Or, this interval (-7 , 4)
Let's pick 0 in the last interval and test it in the inequality
(0 + 7) ( 0 - 4) < 0 ???
(7) (-4) < 0 ???
-28 < 0 and this is true
So......the answer is x = (-7 ,4)
Here's a graph of y = x^2 + 3x - 28 ..... https://www.desmos.com/calculator/rq4hlo0pr0
Notice that the graph is < 0 on the interval (-7, 4)
x^2+3x<28 subtract 28 from each side
x^2 + 3x - 28 < 0 factor
(x + 7) (x - 4) < 0
Our answers will come from either these two invervals {- ∞, -7) and (4, ∞ )
Or, this interval (-7 , 4)
Let's pick 0 in the last interval and test it in the inequality
(0 + 7) ( 0 - 4) < 0 ???
(7) (-4) < 0 ???
-28 < 0 and this is true
So......the answer is x = (-7 ,4)
Here's a graph of y = x^2 + 3x - 28 ..... https://www.desmos.com/calculator/rq4hlo0pr0
Notice that the graph is < 0 on the interval (-7, 4)