Question

The solution set for `0 < − x/3 < 2, x ∈ z` is ______.

Options

• {−5, −4, −3, −2, −1}

• {−6, −5, −4, −3, −2, 1}

• {−5, −4, −3, −2, −1, −0}

• {−6, −5, −4, −3, −2, −1, 0}

Answer 1

The solution set for `0 < − x/3 < 2, x ∈ z` is {−5, −4, −3, −2, −1}.

Explanation:

We are given the inequality 

0 < `−x/3 < 2`

Multiplying all parts by 3, we get

0 < − x < 6.

Multiplying by −1 and reversing the inequality signs,

−6 < x < 0.

Hence, the solution set is {−5, −4, −3, −2, −1}.