Question

What is the solution set for the given inequality if the replacement set for r is {5, 6, 7, 8, 9, 10}? 3r ≤ 4r – 6 A. {6, 7, 8, 9,10} B. {7, 8, 9,10} C. {5} D. {5, 6}

Answer 1

Start with

`3r \leq 4r-6`

Subtract
`3r` from both sides:

`0 \leq r - 6 \iff r-6 \geq 0`

Add 6 to both sides:

`r \geq 6`

So, All numbers greater than or equal to 6 are ok: the solution is the first set:

`A = \{6,\ 7,\ 8,\ 9,\ 10\}`