Question 971159: Solve and graph the solution of the two inequalities
|3x-7|is equal or greater than 23
(X-1)(x+3)(x2)<0
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! |3x-7| >= 23.
if the expression inside the absolute value sign is positive, then the absolute value of the expression is equal to the expression itself.
if the expression insides the absolute value sign is negative, then the absolute value of the expression is equal to the expression iteslf times - 1.
what this means is that you split the problem into two pieces.
you get 3x-7 >= 23 and you get -(3x-7) >= 23
when you take -(3x-7) >= 23 and multiply both sides of that equation by -1, you wind up with 3x-7 <= -23.
so you are dealing with 3x - 7 >= 23 and you are dealing with 3x-7 <= 23
solve 3x-7 >= 23 to get x >= 10.
solve 3x-7 <= -23 to get x <= -16/3
those are your solutions.
for (x-1)(x+3)(x^2) < 0, set it equal and solve for x.
you will get x = 1, x = -3, and x = 0.
those are the transition points in the grpah of that equation.
look at the intervals to the left of x = -3, between -3 and 0, between 0 and 1, and greater than 1.
see if the function is positive or negative in those intervals.
when x = -5, the function is positive.
when x = -1, the function is negative.
when x = .5, the function is negative.
when x = 5, the function is positive.
your solution should be that the function is negative between x = -3 and 0 and between x = 0 and x = 1
this can be written as:
-3 < x < 0 and 0 < x < 1
you can't include -3 or 0 or 1 because the function is < 0 and not <= 0.
here's a graph of the equation of y = (x-1)*(x+4)*(x^2)
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