find the smallest two consecutive integers such that five times the smaller is at least 8 more than three times the larger

Question

Write an inequality and solve

 

Answer 1

Let the larger integer be n, the smaller n-1

5(n-1)≥3n+8

5n-5≥3n+8

2n≥13

n≥6.5, call it 7

n-1=6

5(6)≥21+8

30≥29

Answer 2

n = first number

n + 1 = second number

 

5n ≥ 3(n + 1) + 8

5n ≥ 3n + 3 + 8

2n ≥ 11

n ≥ 5.5

 

The two smallest numbers are 6 and 7.