Question

Solve the following system of inequality:

4x - 9 ≤ 6 + x .......... (i)

12 - 7x ≤ 5 ........... (ii)

and represent the solution on number line.

Answer 1

Inequality: 4x - 9 ≤ 6 + x

⇒ 4x - x ≤ 6 + 9

⇒ 3x ≤ 15

⇒ x ≤ 5 ......... (iii)

Then, inequality 12 - 7x ≤ 5

⇒ 12 - 5 ≤ 7x

⇒ 7 ≤ 7x

⇒ 1 ≤ x

⇒ x ≥ 1 ........ (iv)

From equation (iii) and (iv) required solution is x ∈ [1, 5) as shown on number line.

(Point 5 is not included)