# Linear Inequalities and their Problems

These MCQs help students to learn about the concepts of Linear Inequalities and we will study linear inequalities in one and two variables. The study of inequalities is very useful in solving problems in the field of science, mathematics, statistics, optimization problems, economics, psychology, etc.

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If – 3x + 17 < – 13, then

x ∈ (10, ∞) x ∈ [10, ∞) x ∈ (– ∞, 10] x ∈ [– 10, 10)

Given that x, y and b are real numbers and x < y, b < 0, then

x/b < y/b x/b ≤ y/b x/b > y/b x/b ≥ y/b

If |x −1| > 5, then

x ∈ (– 4, 6) x ∈ [– 4, 6] x ∈ (– ∞, – 4) U (6, ∞) x ∈ [– ∞, – 4) U [6, ∞)

If |x – 7|/(x – 7) ≥ 0, then

x ∈ [7, ∞) x ∈ (7, ∞) x ∈ (– ∞, 7) x ∈ (– ∞, 7]

If | x − 1| > 5, then

x∈(−∞, −4)∪(6, ∞] x∈[6, ∞) x∈(6, ∞) x∈(−∞, −4)∪(6, ∞)

The solution of |2/(x – 4)| > 1 where x ≠ 4 is

(2, 6) (2, 4) ∪ (4, 6) (2, 4) ∪ (4, ∞) (-∞, 4) ∪ (4, 6)

The solution of the inequality |x – 1| < 2 is

(1, ∞) (-1, 3) (1, -3) (∞, 1)

The graph of the inequalities x ≥ 0, y ≥ 0, 2x + y + 6 ≤ 0 is

a square a triangle { } none of these

Solve: 2x + 1 > 3

[-1, ∞] (1, ∞) (∞, ∞) (∞, 1)

The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then

Length < 20 cm

Length ≤ 20 cm

If (|x| – 1)/(|x| – 2) ‎≥ 0, x ∈ R, x ‎± 2 then, the interval of x is

(-∞, -2) ∪ [-1, 1]

[-1, 1] ∪ (2, ∞)

(-∞, -2) ∪ (2, ∞)

(-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

If x² &lt; -4 then, the value of x is

(-2, 2)

(2, ∞)

(-2, ∞)

No solution

If -2 &lt; 2x – 1 &lt; 2 then, the value of x lies in the interval

(1/2, 3/2)

(-1/2, 3/2)

(3/2, 1/2)

(3/2, -1/2)

The graph of the inequations x ≤ 0 , y ≤ 0, and 2x + y + 6 ≥ 0 is

Exterior of a triangle

A triangular region in the 3rd quadrant

None of these

If |x| &lt; -5 then, the value of x lies in the interval

(-∞, -5)

(∞, 5)

(-5, ∞)

No Solution

Quiz/Test Summary
Title: Linear Inequalities and their Problems
Questions: 16
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