Question

The solution of the inequation, `2x - 7/2 > 5/2 - x, x ∈ N,` is ______.

Options

• {3, 4, 5, 6, ...}

• {2, 3, 4, ...}

• {1, 2}

• no solution

Answer 1

The solution of the inequation, `2x - 7/2 > 5/2 - x, x ∈ N,` is {3, 4, 5, 6, ...}.

Explanation:

`2x - 7/2 > 5/2 - x, x ∈ N`

Add x to both sides and add `7/2`​ to both sides:

`2x + x > 5/2 + 7/2`

`3x > 12/2 = 6`

x > 2

Use the replacement set x ∈ N = {1, 2, 3, …}

Values of x satisfying x > 2:

{3, 4, 5, 6, …}