Represent the inequality, 3 x + 1 ≥ - 5 on a real number line.

Given, 3 x + 1 ≥ - 5 ⇒ 3 x ≥ - 5 - 1 (Transferring positive term on other side) ⇒ 3 x ≥ - 6 ⇒ x ≥ - 2 (Dividing inequation by a positive number) The solution of given inequality on number line is,

Represent the inequality, 3 x + 1 ≥ - 5 on a real number line.

Given, 3 x + 1 ≥ - 5 ⇒ 3 x ≥ - 5 - 1 (Transferring positive term on other side) ⇒ 3 x ≥ - 6 ⇒ x ≥ - 2 (Dividing inequation by a positive number) The solution of given inequality on number line is,

Represent the inequality, 2 ( 2 x - 3 ) ≤ 6 on real number line.

Given, 2 ( 2 x - 3 ) ≤ 6 ⇒ 2 x - 3 ≤ 3 (Dividing inequation by a positive number) ⇒ 2 x ≤ 3 + 3 (Transferring negative term on other side) ⇒ 2 x ≤ 6 ⇒ x ≤ 3 (Dividing inequation by a positive number) Hence, the solution of given inequality on number line is,

Represent the inequality, - 2 ≤ x < 5 on a real number line.

Given that, - 2 ≤ x < 5 ⇒ x is greater than equal to - 2 and less than 5 . Thus, solution of this inequality will be numbers lying right side of the - 2 and left side of the 5 on real number line including - 2 but excluding 5 . Hence, the solution of given inequality on number line is given as,

Represent the inequality 8 ≥ x > - 3 on a real number line.

Given that, 8 ≥ x > - 3 ⇒ x is less than equal to 8 and greater than - 3 . Thus, solution of this inequality will be numbers lying right side of the - 3 and left side of the 8 on real number line excluding - 3 but including 8 . Hence, the solution of given inequality on number line is,

Represent the inequality - 5 < x ≤ - 1 on a real number line.

Given that, - 5 < x ≤ - 1 ⇒ x is greater than - 5 and less than equal to - 1 . Thus, solution of this inequality will be numbers lying right side of the - 5 and left side of the - 1 on real number line excluding - 5 but including - 1 . Hence, the solution of given inequality on number line is,