Solve and graph the solution set on a number line. 8 x - 9 ≥ 35 - 3 x ; x ∈ N

Given, 8 x - 9 ≥ 35 - 3 x ; x ∈ N ⇒ 8 x + 3 x ≥ 35 + 9 ⇒ 11 x ≥ 44 ⇒ x ≥ 44 11 ⇒ x ≥ 4 Natural numbers, N = 1 , 2 , 3 , 4 , 5 , . . . . . . . . . . . . Therefore, the solution set is 4 , 5 , 6 , 7 , 8 , . . . . . . . . . . . . . . . Hence, the graph of the number line is shown below, and the dots represent the solution set.

Solve and graph the solution set on a number line. 2 x 5 + 1 < - 3 ; x ∈ R

Given, 2 x 5 + 1 < - 3 ; x ∈ R ⇒ 2 x 5 < - 3 - 1 ⇒ 2 x 5 < - 4 ⇒ 2 x < - 4 × 5 ⇒ 2 x < - 20 ⇒ x < - 20 2 ⇒ x < - 10 Therefore, the solution set is . . . . . . . . , - 13 , - 12 , - 11 , - 10 . Hence, the graph of the number line is shown below, and the dots represent the solution set.

Solve and graph the solution set on a number line. x 2 > - 1 + 3 x 4 ; x ∈ N

Given, x 2 > - 1 + 3 x 4 ; x ∈ N ⇒ x 2 > - 4 + 3 x 4 ⇒ 4 x > 2 - 4 + 3 x ⇒ 4 x > - 8 + 6 x ⇒ 8 > 6 x - 4 x ⇒ 8 > 2 x ⇒ x < 8 2 ⇒ x < 4 Natural number, N = 1 , 2 , 3 , 4 , 5 , 6 , . . . . . . . . . . . . . Therefore, the solution set is 1 , 2 , 3 . Hence, the graph of the number line is shown below, and the dots represent the solution set.

Solve and graph the solution set on a number line 2 3 x + 5 ≤ 1 2 x + 6 ; x ε W

A line of infinite extent whose points correspond to the real numbers according to their distance in a positive or negative direction from a point arbitrarily taken as zero. Given, 2 3 x + 5 ≤ 1 2 x + 6 ; x ε W 2 x + 15 3 ≤ 1 x + 12 2 2 2 x + 15 ≤ x + 12 3 4 x + 30 ≤ 3 x + 36 Arrange the constants and variables on each side. 4 x - 3 x ≤ 36 - 30 x ≤ 6 Hence, this is the required answer.