Question

Solve, write your answer in interval notation and graph the solution set.

15a. 2x^2-5x less than or equal to 3

15b. (x+3)/(x-4) greater than 0

Answer 1

15a. 2x^2 - 5x<= 3


2x^2 - 5x -3<= 0

Let us solve the equation
2x^2 - 5x -3 =0
D = 25 + 4 * 2* 3 = 49 = 7^2
x1 =(5-7)/(2*2) = -2/4 = -1/2 = -0.5
x2 =(5+7)/(2*2) = 12/4 = 3

As the coefficient at x^2 is 2>0, the branches of theparabola directed upward, and so the solution of the eqaution is
[-0.5, 3]

Answer: [-0.5, 3]


-------------------*=============================*-------------------->
-0.5 3
the ends are included, and the solution is shown with====




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15b. (x+3)/(x-4) > 0

This inequality reduces to the following system:
(x+3)(x-4)>0
and
x-4 <> 0


The solution of the first inequality:

(x+3)(x-4)>0

x in(-infinity, -3) U (4, +infinity)

Since this set does not contain 4, it is a solution ofthe initial system


Answer: (-infinity, -3) U (4, +infinity)

================o---------------------o===============================>
-3 4
the ends are not included, and the solution is shown with====