Sol : Option B
The critical points are x = 1/3, 5/4
Plot these points on the number line,
[image]
The given inequality is positive, the solution is x ε (-∞, 1/3)∪(5/4, ∞)
Q.2. Solve the inequality 3x-8/x+7>8
A. -64/5, -7
B. -7, 0
C. -7, 7
D. None of these
Sol : Option B
[image]
The solution is x ε (-64/5, -7)
Q.3. Solve the inequality 1/x+3≤11
A. (-∞ -3) ∪ [-32/11, ∞)
B. (-3, -32/11)
C. (-3, 8)
D. (-15, 0)
Sol : Option A
The critical points are x = -3, -32/11
[image]
The solution is (-∞, -3) ∪ (-32/11, ∞)
Q.4. Solve the inequality 2x-1/x+3 > -5
A. (-∞, -3) ∪ (-2, 0)
B. (-3, -2)
C. (-∞, 5)
D. (-∞, -3) ∪ (-2, ∞)
Sol : Option A
The critical points are x = -3, -2
[image]
The solution is (-∞, -3) ∪ (-2, ∞)
Q.5. Solve |x + 7| < 11
A. 0 < x < 4
B. – 18 < x < 4
C. x > 4
D. -18 < x < 0
Sol : Option B
We have |x + 7| < 11
⇒ -11 < x + 7 < 11 ⇒ - 18 < x < 4
Sol : Option A
(x+2)(x-7)/(x+3)2≥0
The critical points are x = -3, -2, 7
Plot these points on the number line and draw curve.
[image]
The solution is x ε (-∞, -3) ∪ (-3, -2) ∪ (7, ∞)
Q9. Solve the inequality (x + 4)2 (x – 3) < 0
A. (3, ∞)
B. (-4, 3)
C. (-∞, -4) ∪ (-4, 3)
D. (-∞, 3)
Sol : Option C
We have (x + 4)2 (x – 3) < 0
The critical points are x = -4, 3
[image]
The sol. is (-∞, -4) ∪ (-4, 3)
Q10. Solve the inequality 1/(x+3) ≤ 1/(2x+3)
A. (-3, 2) ∪ (2, ∞)
B. (-5/2), 3)
C. (-∞, -5/2) ∪ (3, 7)
D. (-∞, -3) ∪ (-5/2, -2)
Sol : Option B
The critical points are x = -3, -5/2, -2
[image]
The solution is (-∞, -3) ∪ (-5/2, -2)