3 < x < 4
-4 < x < -3
-2 < x < -1
-3 < x < 0
Correct answer is B
\(\frac{x + 1}{3}\) > \(\frac{1}{X + 3}\) = \(\frac{x + 1}{3}\) > \(\frac{x + 3}{X + 3}\)
= (x + 1)(x + 3)2 > 3(x + 3) = (x + 1)[x2 + 6x + 9] > 3(x + 3)
x3 + 7x2 + 15x + 9 > 3x + 9 = x3 + 7x2 + 12x > 0
= x(x + 3)9x + 4) > 0
Case 1 (+, +, +) = x > 0 , x + 3 > 0, x + 4 > 0
= x > -4 (solution only)
Case 2 (+, -, -) = x > 0, x + 4 < 0
= x > 0, x < -3, x < -4 = x < -3(solution only)
Case 3 (-, +, -) = x < 0, x > -3, x < -4 = x < -0, -4 < x < 3(solutions)
Case 4 (-, -, +) = x < 0, x + 3 < 0, x + 4 > 0
= x < 0, x < -5, x > -4 = x < -0, -4 < x < -3(solution)
combining the solutions -4 < x < -3
What is the value of p if the gradient of the line joining (-1,p) and (p, 4) is 23?...
This table below gives the scores of a group of students in a Further Mathematics Test. Score...
Find the exterior angle of a 12 sided regular polygon ...
Find the radius of a sphere whose surface area is 154 cm\(^2\)? ...
A rectangle with width \(\frac{3}{4}\)cm and area 3 \(\frac{3}{8}\)cm\(^2\). Find the length...
Find the values of x for which the expression \(\frac{(x - 3)(x - 2)}{x^2 + x - 2}\)...
Given that P = x2 + 4x - 2, Q = 2x - 1 and Q - p = 2, find x...
Solve the inequality y2 - 3y > 18...
If a : b = 5 : 8, x : y = 25 : 16; evaluate \(\frac{a}{x}\) : \(\frac{b}{y}\)...