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
1
Expert's answer
2013-01-24T08:00:46-0500
2x^2 - 5x <=3 First solve the equation 2x^2 - 5x = 3 2x^2 - 5x - 3 =0 D = 25 + 4*2*3= 49 = 7^2 x1 =(5-7)/(2*2) = -2/4 = -0.5 x2 =(5+7)/(2*2) = 12/4 = 3 As the coefficient at x^2 is 2>0 he branches of theparabola y = 2x^2 - 5x -3 are directed upwards, whence the inequality 2x^2 - 5x <=3 Has the following solution x belongs to[-0.5, 3] Solution set: --------*===========================*---------------> -0.5 3
Here ===== means solution interval, and * means that the corresponding point belogns to thatinterval15b. (x+3)/(x-4) greater than 0 Solution: (x+3)/(x-4)> 0 This inequality is equivalent to the following system: (x+3)(x-4)>0 x-4 <>0 ( <> means not equal ) (x+3)(x-4)>0 x <>4 ( <> means not equal ) This first inequality has the solution x in (-3,4) and this does not contains the point 4, so (-3,4) is the solution of the initial inequality Solution set: --------o====================o---------------> -3 4
Here ===== means solution interval, and o means that the corresponding point does not belongto that interval
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