#1**+10 **

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)

CPhill
Apr 7, 2015

#1**+10 **

Best Answer

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)

CPhill
Apr 7, 2015