Question

The solution set for inequation 3(7 − x) ≥ 15 − 7x > `(x+1)/3, x ∈ R` is ______.

Options

• `-3/2 < x<2`

• `-3/2 <= x <= 2`

• `-3/2 < x <= 2`

• `-3/2 <= x < 2`

Answer 1

The solution set for inequation 3(7 − x) ≥ 15 − 7x > `(x+1)/3, x ∈ R` is `\underline(-3/2 <= x < 2)`.

Explanation:

`3(7 − x) ≥ 15 − 7x > (x+1)/3`

3(7 − x) ≥ 15 − 7x

⇒ 21 − 3x ≥ 15 − 7x

⇒ 4x ≥ −6

⇒ x ≥ −3/2

`15 − 7x > (x+1)/3`

⇒ 45 − 21x > x + 1

⇒ −22x > −44

⇒ x < 2

Combine:

`−3/2 ≤ x < 2`