+23254 x(3x - 4) ≤ (6x² - 3x + 5) / 10
Simplify:
3x² - 4x ≤ (6x² - 3x + 5) / 10
30x² - 40x ≤ 6x² - 3x + 5
24x² - 37x - 5 ≤ 0
Factoring: (8x + 1)(3x - 5) ≤ 0
This divides the number line into three parts: x < -1/8, -1/8 < x < 5/3, x > 5/3
Try a a number in the lower region: I tried -1: [8(-1) + 1][3(-1) - 5] = 56. Since this is not less than or equal to zero, all numbers less than -1/8 will not work.
Try a number in the middle region: I tried 0: [8(0) + 1][3(0) - 5] = -5. Since this is less than zero, all numbers in this region work. Answer: -1/8 < x < 5/3
Try a a number in the upper region: I tried 2: [8(2) + 1][3(2) - 5] = 17. Since this is not less than or equal to zero, all numbers greater than 5/3 will not work.
Now, to answer the question, you will have to figure out (count) the number of integers in the region
-1/8 < x < 5/3.
- See more at: http://web2.0calc.com/questions/help-please_45#sthash.fDB7TCoS.dpuf
+23254 x(3x - 4) ≤ (6x² - 3x + 5) / 10
Simplify:
3x² - 4x ≤ (6x² - 3x + 5) / 10
30x² - 40x ≤ 6x² - 3x + 5
24x² - 37x - 5 ≤ 0
Factoring: (8x + 1)(3x - 5) ≤ 0
This divides the number line into three parts: x < -1/8, -1/8 < x < 5/3, x > 5/3
Try a a number in the lower region: I tried -1: [8(-1) + 1][3(-1) - 5] = 56. Since this is not less than or equal to zero, all numbers less than -1/8 will not work.
Try a number in the middle region: I tried 0: [8(0) + 1][3(0) - 5] = -5. Since this is less than zero, all numbers in this region work. Answer: -1/8 < x < 5/3
Try a a number in the upper region: I tried 2: [8(2) + 1][3(2) - 5] = 17. Since this is not less than or equal to zero, all numbers greater than 5/3 will not work.
Now, to answer the question, you will have to figure out (count) the number of integers in the region
-1/8 < x < 5/3.
- See more at: http://web2.0calc.com/questions/help-please_45#sthash.fDB7TCoS.dpuf
