Question

If `(3x)/5 - (2x-1)/3 > 1, x ∈ l` then solution set is ______.

Options

• {x : x < −10, x ∈ l}

• {x : x ≤ −10, x ∈ l}

• {x : x > −10, x ∈ l}

• {x : x ≥ −10, x ∈ l}

Answer 1

If `(3x)/5 - (2x-1)/3 > 1, x ∈ l` then solution set is {x : x < −10, x ∈ l}.

Explanation:

`(3x)/5 - (2x-1)/3 > 1`

Common denominator 15:

`(9x - (10x - 5))/15 > 1 (-x + 5)/15 > 1`

Multiply by 15: 

−x + 5 > 15

−x > 10

x < −10

So the set (for x in the integers) is {x : x < −10, x ∈ I}