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Inequalities : Practice Problems
Solve the given practice questions based on inequalities. Also, the answer key and explanations are given for the same.
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Q.1.
Solve the inequality 7x+5/3x-5<5.
A. (1/3, 0)
B. (-∞, 1/3)∪(5/4, ∞)
C. (1/3, 5/4)
D. (-∞, 1/3)∪(5/4, 7)
Answer & Explanation
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Sol : Option
B
The critical points are x = 1/3, 5/4
Plot these points on the number line,
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
Answer & Explanation
Sol : Option
B
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)
Answer & Explanation
Sol : Option
A
The critical points are x = -3, -32/11
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, ∞)
Answer & Explanation
Sol : Option
A
The critical points are x = -3, -2
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
Answer & Explanation
Sol : Option
B
We have |x + 7| < 11
⇒ -11 < x + 7 < 11 ⇒ - 18 < x < 4
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Inequalities: Practice Problems
Q.6.
Solve |2x + 5| < 14
A. 0 < x < 5
B. -19/2 < x < 0
C. -19/2 < x < 9/2
D. 0 < x < 9/2
Answer & Explanation
Sol : Option
C
We have |2x + 5| < 14
⇒ -14 < 2x + 5 < 14
⇒ -19 < 2x < 9 ⇒ -19/2 < x < 9/2
Q.7.
Solve |5x + 5| - 8 ≤ 17
A. -5 ≤ x ≤ 5
B. -5 ≤ x ≤ 4
C. 0 ≤ x ≤ 4
D. - 6 ≤ x ≤ 4
Answer & Explanation
Sol : Option
D
We have |5x + 5| - 8 ≤ 17 ⇒ |5x + 5| ≤ 25 ⇒ -25 < 5x + 5 ≤ 25 ⇒ - 30 < 5x ≤ 20 ⇒ - 6 ≤ x ≤ 4
Q8.
Solve the inequality (x+2)(x-7)/(x+3)
2
≥0
A. (-∞, -3) ∪ (-3, -2) ∪ (7, ∞)
B. (-∞, -3) ∪ (7, ∞)
C. (-3, -2)
D. (7, ∞)
Answer & Explanation
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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.
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)
Answer & Explanation
Sol : Option
C
We have (x + 4)
2
(x – 3) < 0
The critical points are x = -4, 3
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)
Answer & Explanation
Sol : Option
B
The critical points are x = -3, -5/2, -2
The solution is (-∞, -3) ∪ (-5/2, -2)
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