Fill in the blanks with correct inequality sign (>, <, ≥, ≤).

(i) 5x < 20 ⇒ x ………. 4

(ii) –3x > 9 ⇒ x ………. –3

(iii) 4x > –16 ⇒ x ………. –4

(iv) –6x ≤ –18 ⇒ x ………. 3

(v) x > –3 ⇒ –2x ………. 6

(vi) a < b and c > 0 ⇒ ……….

(vii) p – q = –3 ⇒ p ………. q

(viii) u – v = 2 ⇒ u ………. V

Solve each of the following in equations and represent the solution set on the number line.

6x ≤ 25, where (i) x ϵ N, (ii) x ϵ Z.

Solve each of the following in equations and represent the solution set on the number line.

–2x > 5, where (i) x ϵ Z, (ii) x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

3x + 8 > 2, where (i) x ϵ Z, (ii) x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

5x + 2 < 17, where (i) x ϵ Z, (ii) x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

3x – 4 > x + 6, where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

3 – 2x ≥ 4x – 9, where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

, where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

Solve each of the following in equations and represent the solution set on the number line.

where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

, where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

, where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

, where x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

.

Solve each of the following in equations and represent the solution set on the number line.

.

Solve each of the following in equations and represent the solution set on the number line.

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Solve each of the following in equations and represent the solution set on the number line.

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Solve each of the following in equations and represent the solution set on the number line.

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Solve each of the following in equations and represent the solution set on the number line.

.

Solve each of the following in equations and represent the solution set on the number line.

.

Solve each of the following in equations and represent the solution set on the number line.

3x – 7|> 4, x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

5 – 2x| ≤ 3, x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

.

Solve each of the following in equations and represent the solution set on the number line.

, x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

< 2, x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

< 2, x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

< 0, x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

≥ 0, x ϵ R. –{–2, 2}

Solve each of the following in equations and represent the solution set on the number line.

1, x ϵ R – {–2, 2}

Solve each of the following in equations and represent the solution set on the number line.

|x + a| + |x| > 3, x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.

x - 4 > 1, x ≠ 4.

Solve the following systems of linear in equations:

, x > 0

Solve the following systems of linear in equations:

–11 ≤ 4x – 3 ≤ 13

Solve the following systems of linear in equations:

5x – 7 < (x + 3), 1 –x – 4

Solve the following systems of linear in equations:

–2 < < 7

Solve the following systems of linear in equations:

3x – x > x + > 3

Solve the following systems of linear in equations:

+ 11 < 0

Solve the following systems of linear in equations:

–12 < 4 – ≤ 2

Solve the following systems of linear in equations:

1 ≤ |x – 2| ≤ 3

Find all pairs of consecutive even positive integers both of

which are larger than 8 such that their sum is less than 25.

Find all pairs of consecutive even positive integers both of

which are larger than 8 such that their sum is less than 25.

A company manufactures cassettes. Its cost and revenue function are C(x) = 25000 + 30x and R(x) = 43x respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?

The watering acidity in a pool is considered normal when the average pH reading of three daily measurements is between 8.2 and 8.5. If the first two pH reading 8.48 and 8.35, find the range of the pH values for the third reading that will result in the acidity level is normal.

A manufacturer has 640 litres of an 8% solution of boric acid. How many litres of 2% boric and acid solution be added to it so that the boric acid content in the resulting mixture will be more than 4% but less than 6%.

How many litres of water will have to be added to 600 litres of the 45% solution of acid so that the resulting mixture will contain more than 25%, but less than 30% acid content?

To receive grade A in a course one must obtain an average of 90 marks or more in five papers, each of 100 marks. If Tanvy scored 89, 93, 95 and 91 marks in first four papers, find the minimum marks that she must score in the last paper to get grade A in the course.

Find the solution set of the inequation |x – 1| < 2.

Find the solution set of the inequation |2x – 3| < 1.

Find the solution set of the inequation < 0. x ≠ 2

Find the solution set of the inequation < 1.

Solve the system of inequation x – 2 ≥ 0, 2x – 5 ≤ 3.

Solve –4x > 16, when x ϵ Z.

Solve x + 5 > 4x – 10, when x ϵ R.

Solve < 1, when x ϵ R.

Solve , when x ϵ R.

Solve |x| < 4, when x ϵ R.

Solve |x| > 4, when x ϵ R.