1 a Spt Solve the inequality and give your answer in interva

1. (a) (Spt) Solve the inequality and give your answer in interval notation: 13-4x ss (b) (Sp) Determine the 7th term in the binomial expansion of (3p + q4)12 .

Solution

a. | 3-4x|<=5

3-4x<=5 , 3-4x>=-5

-4x<=2 , -4x>=-8

x>=-1/2, x<=2

[-1/2,2]

b. (3p +q⁴)¹²

nth term of (x+y)ⁿ is given by

n C r(x)^n-ry^r

So the 7^th term is

12C7(3p)^12-7(q⁴)⁷

=792(3p)⁵q²⁸

=192456 p⁵q²⁸