# Linear Inequations

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• Q1

|x| > 3 implies that

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x < -3 or x > 3.

##### Explanation:

If a is a positive real number then

|x| > a x < -a or x > a.

• Q2

Rama has Rs 500 and wants to buy some books and pens. The cost of one book is Rs 110 and that of a pen is Rs 20. If ‘x’ denotes the number of books and ‘y’ denotes the number of pens and the total amount spent by him is Rs (110x + 20y), then the linear inequality for this situation will be

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##### Explanation:
• Q3

Rohan wants to cut three lengths from a board of length 91 cm whose second length is to be 3 cm longer than the shortest and third length is to be twice as long as the shortest. The possible lengths for the shortest board if third piece is to be at least 5 cm longer than the second is

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##### Explanation:
• Q4

If the point (x, 2) satisfies the inequality
- 4x + 5y ≤ 14, then the smallest possible value of x is

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– 1.

##### Explanation:

Put y = 2 in the given inequality to find the value of x, i.e.,

– 4x + 5 × 2 ≤ 14

– 4x ≤ 4
x ≥ – 1

• Q5

Inequalities x - 2y - 2 graphically represented by two dimensional plane, is

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