What number line represents the solution set for the inequality 3x < –9?
2 answers:
<h2>Answer:</h2>
The solution set of the given inequality is:
(-∞,-3)
<h2>Step-by-step explanation:</h2>We are given a inequality in terms of the variable x by:
We divide both side of the inequality by 3 to obtain the new expression as:
This means that the graph of such a inequality is the set of all the real value which are strictly less than -3( since the inequality is strict)
Hence, the solution set in set-Builder form is:
={all x belonging to real numbers| x<-3}
and in interval form the solution is: (-∞,-3)
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First of all, when I do all the math on this, I get the coordinates for the max point to be (1/3, 14/27). But anyway, we need to find the derivative to see where those values fall in a table of intervals where the function is increasing or decreasing. The first derivative of the function is 
. Set the derivative equal to 0 and factor to find the critical numbers. 
, so x = -3 and x = 1/3. We set up a table of intervals using those critical numbers, test a value within each interval, and the resulting sign, positive or negative, tells us where the function is increasing or decreasing. From there we will look at our points to determine which fall into the "decreasing" category. Our intervals will be -∞<x<-3, -3<x<1/3, 1/3<x<∞. In the first interval test -4. f'(-4)=-13; therefore, the function is decreasing on this interval. In the second interval test 0. f'(0)=3; therefore, the function is increasing on this interval. In the third interval test 1. f'(1)=-8; therefore, the function is decreasing on this interval. In order to determine where our points in question fall, look to the x value. The ones that fall into the "decreasing" category are (2, -18), (1, -2), and (-4, -12). The point (-3, -18) is already a min value.