Question

The set of real x satisfying the inequality `(5 - 2x)/3 ≤ x/6 - 5` is [a, ∞). The value of ‘a’ is ______.

Options

• 2

• 4

• 6

• 8

Answer 1

The set of real x satisfying the inequality `(5 - 2x)/3 ≤ x/6 - 5` is [a, ∞). The value of ‘a’ is 8.

Explanation:

`(5 - 2x)/3 ≤ x/6 - 5`

`\implies (5 - 2x)/3 ≤ (x - 30)/6`

`\implies 5 - 2x ≤ (x - 30)/2`

`\implies` 10 – 4x ≤ x –30

`\implies` 40 ≤ 5x

`\implies` 8 ≤ x

`\implies` x ∈ [8, ∞)