solve and check (3n+3)/7>=(n+4)/5

Question

Solve for n.

Answer 1

The inequality is (3n + 3)/7 ≥ (n + 4)/5

5(3n + 3) ≥ 7(n + 4)

15n + 15 ≥ 7n + 28

15n - 7n ≥ 28 - 15

8n ≥ 13

n ≥ 13/8

n ≥ 1.625.

Solution set is {n | n ≥ 1.625}.

Check :

Substitute the value n = 1.7 in (3n + 3)/7 ≥ (n + 4)/5.

(3(1.7) + 3)/7 ≥ (1.7 + 4)/5

8.1/7 ≥ 5.7/5

1.157 ≥ 1.14.

The above statement is true, so {n | n ≥ 1.625} is a solution set of (3n + 3)/7 ≥ (n + 4)/5.