Question

Solve the inequation = 12 + `1(5)/(6)` ≤ 5 + 3x, x ∈ R. Represent the solution on a number line.

Answer 1

12 + `1(5)/(6)x` ≤ 5 + 3x

⇒ 12 + `(11)/(6)x` ≤ 5 + 3x
⇒ 72 + 11x ≤ 30 + 18x   ...(Multiplying by 6)
⇒ 11x - 18x ≤ 30 - 72
⇒ -7x ≤ - 42

⇒ -x ≤ - `(42)/(7)`
⇒ -x ≤ - 6
⇒ x ≥ 6
∴ x ∈ R
∴ Solution set = {x : x ∈ R, x ≥ 6}
Solution set on Number line