Given, 6x + 2(6 - x) > 2x - 2 < 5x/2 - 3x/4, then x can take which of the following values?
1). 9
2). -8
3). 5
4). -9
⇒ 6x + 2(6 - x) > 2x - 2
⇒ 6x + 12 - 2x > 2x - 2
⇒ 2x > - 14
⇒ x > - 7 ----(1)
⇒ 2x - 2 < 5x/2 - 3x/4
⇒ 2x - 2 < 7x/4
⇒ 8x - 7x < 8
⇒ x < 8 ----(2)
From (1) and (2),
- 7 < x < 8
∴ x = 5 satisfies the given conditions from the above options.4. If $-\frac{3}{2} + \left(\frac{2}{3}\right)(3x + 9) = $\frac{x}{2}$, then what is the value of x?
5. If 2x - 3(2x - 2) > x - 1 < 2 + 2x; then x can take which of the following values?
6. What is the difference of the factors of the expression $x^{2}+ \left(\frac{1}{x^{2}}\right) - 6$
8. In an arithmetic progression if 13 is the 3rd term, 47 is the 13th term, then 17 is which term?
9. .If a + b = 10 and ab = 21, then the value of $(a-b)^{2}$ is