Solve 2 x - 2 < 3 x - 2 , x ∈ - 3 , - 2 , - 1 , 0 , 1 , 2 , 3

Given inequation is 2 x - 2 < 3 x - 2 Grouping the terms on same sides, we will get, 2 x - 2 < 3 x - 2 2 x - 4 < 3 x - 2 2 x - 3 x < - 2 + 4 - x < 2 On multiplying - 1 both sides, the inequality will reverse. x > - 2 As x ∈ - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 The solution set is - 1 , 0 , 1 , 2 , 3

Solve 2 x - 2 < 3 x - 2 , x ∈ - 3 , - 2 , - 1 , 0 , 1 , 2 , 3

Given inequation is 2 x - 2 < 3 x - 2 Grouping the terms on same sides, we will get, 2 x - 2 < 3 x - 2 2 x - 4 < 3 x - 2 2 x - 3 x < - 2 + 4 - x < 2 On multiplying - 1 both sides, the inequality will reverse. x > - 2 As x ∈ - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 The solution set is - 1 , 0 , 1 , 2 , 3

If x is a negative integer, then find the solution set of 2 3 + 1 3 ( x + 1 ) > 0 .

Given, x is a negative integer. 2 3 + 1 3 ( x + 1 ) > 0 ⇒ x + 1 3 > - 2 3 ⇒ x + 1 > - 2 ⇒ x > - 3 As is x is negative integer so x < 0 and from above x > - 3 so allowed values for x are - 1 and - 2 Hence, solution is x = { - 1 , - 2 }

Solve x - 3 2 + x > 2 3 x - 1 , x ∈ - 3 , - 2 , - 1 , 0 , 1 , 2 . Also represent its solution on the number line.

Given inequation is x - 3 2 + x > 2 3 x - 1 Grouping the terms on same sides, we will get, x - 6 - 3 x > 6 x - 2 - 2 x - 6 > 6 x - 2 - 2 x - 6 x > - 2 + 6 - 8 x > 4 On multiplying - 1 both sides, the inequality will reverse. x < - 4 8 x < - 1 2 As x ∈ - 3 , - 2 , - 1 , 0 , 1 , 2 The solution set is - 1 , - 2 , - 3

Given x ∈ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 9 , solve x - 3 < 2 x - 1 .

Given inequation is x - 3 < 2 x - 1 Grouping the terms on same sides, we will get, x - 2 x < - 1 + 3 - x < 2 On multiplying - 1 both sides, the inequality will reverse. x > - 2 As x ∈ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 9 The solution set is 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9

List the solution set of the inequation 1 2 + 8 x > 5 x - 3 2 , x ∈ Z .

Given inequation is 1 2 + 8 x > 5 x - 3 2 Grouping the terms on same sides, we will get, 8 x - 5 x > - 3 2 - 1 2 3 x > - 3 - 1 2 3 x > - 4 2 3 x > - 2 x > - 2 3 As x ∈ Z The solution set is 0 , 1 , 2 , 3 , 4 , 5 , . . . . . . . .

List the solution set of 11 - 2 x 5 ≥ 9 - 3 x 8 + 3 4 , x ∈ N .

Given inequation is 11 - 2 x 5 ≥ 9 - 3 x 8 + 3 4 Grouping the terms on same sides, we will get, 11 - 2 x 5 ≥ 9 - 3 x + 6 8 11 - 2 x 5 ≥ 15 - 3 x 8 8 11 - 2 x ≥ 5 15 - 3 x 88 - 16 x ≥ 75 - 15 x - 16 x + 15 x ≥ 75 - 88 - x ≥ - 13 On multiplying - 1 both sides, the inequality will reverse. x ≤ 13 As x ∈ N The solution set is 1 , 2 , 3 , 4 , 5 , . . . . . . . . , 13

Find the values of x , which satisfy the inequation: - 2 ≤ 1 2 - 2 x 3 ≤ 1 5 6 , x ∈ N Graph the solution on the number line.

Given that, - 2 ≤ 1 2 - 2 x 3 ≤ 1 5 6 , x ∈ N ⇒ - 2 ≤ 1 2 - 2 x 3 and 1 2 - 2 x 3 ≤ 11 6 ⇒ - 2 - 1 2 ≤ - 2 x 3 and - 2 x 3 ≤ 11 6 - 1 2 ⇒ - 5 2 ≤ - 2 x 3 and - 2 x 3 ≤ 8 6 ⇒ - 15 ≤ - 4 x and - 2 x ≤ 4 ⇒ 15 ≥ 4 x and 2 x ≥ - 4 ⇒ 15 4 ≥ x and x ≥ - 4 2 ⇒ 3 . 75 ≥ x and x ≥ - 2 Hence, - 2 ≤ x ≤ 3 . 75 Thus, the solution set is 1 , 2 , 3 since x ∈ N . The solution on number line is given as

If x ∈ W , find the solution set of 3 5 x - 2 x - 1 3 > 1 . Also graph the solution set on the number line, if possible.

Given inequation is 3 5 x - 2 x - 1 3 > 1 Grouping the terms on same sides, we will get, 3 3 x 15 - 5 2 x - 1 15 9 x - 10 x + 5 15 > 1 9 x - 10 x + 5 > 15 - x > 15 - 5 - x > 10 On multiplying - 1 both sides, the inequality will reverse. x < - 10 As x ∈ W The solution set is null set. Thus, it can not be represent on number line because solution set is null set.

Solve: x 2 + 5 ≤ x 3 + 6 , where x is a positive odd integer.

Given inequation is x 2 + 5 ≤ x 3 + 6 Taking LCM on both side x + 10 2 ≤ x + 18 3 3 x + 10 ≤ 2 x + 18 3 x + 30 ≤ 2 x + 36 3 x - 2 x ≤ 36 - 30 x ≤ 6 As x is a positive odd integer The solution set is 1 , 3 , 5

Solve the following inequality, write down the solution set and represent it on the real number line: - 2 + 10 x ≤ 13 x + 10 < 24 + 10 x , x ∈ Z

- 2 + 10 x ≤ 13 x + 10 and 13 x + 10 < 24 + 10 x Taking - 2 + 10 x ≤ 13 x + 10 , Adding 2 on both the sides - 2 + 10 x + 2 ≤ 13 x + 10 + 2 10 x ≤ 13 x + 12 Subtracting 13 x from both the sides 10 x - 13 x ≤ 13 x + 12 - 13 x - 3 x ≤ 12 x ≥ - 4 Now, taking 13 x + 10 < 24 + 10 x Subtracting 10 from both the sides 13 x + 10 - 10 < 24 + 10 x - 10 13 x < 14 + 10 x Subtracting 10 x from both the sides 13 x - 10 x < 14 + 10 x - 10 x 3 x < 14 x < 14 3 x < 4 . 667 Taking intersection of both the results(on combining both the inequalities) - 4 ≤ x < 4 . 667 Since x belongs to Z (integers) Value of x will be { - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 } Representing the solution set on number line-