Solve the inequation: 5 x - 2 ≤ 3 3 - x , where x ∈ - 2 , - 1 , 0 , 1 , 2 , 3 , 4 . Also represent its solution on the number line.

Given inequation, 5 x - 2 ≤ 3 3 - x ⇒ 5 x - 2 ≤ 9 - 3 x ⇒ 5 x + 3 x ≤ 9 + 2 ⇒ 8 x ≤ 11 ⇒ x ≤ 11 8 As x ∈ - 2 , - 1 , 0 , 1 , 2 , 3 , 4 The solution set is - 2 , - 1 , 0 , 1 Representing the solution on a number line:

Find the solution set of the inequation: x + 5 ≤ 2 x + 3 , x ∈ R . Graph the solution set on the number line.

Given inequation, x + 5 ≤ 2 x + 3 ⇒ x - 2 x ≤ 3 - 5 ⇒ - x ≤ - 2 ⇒ x ≥ 2 As x ∈ R Thus, the solution set is 2 , 3 , 4 , 5 , . . . . . Representing the solution on a number line:

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-