3k (x+2) + 2 = 5x+8

How do I solve for k while keeping x smaller then 3?

k = (5x+6) / (3x+6) and k<3/5

Step-by-step explanation:

3k (x+2) + 2 = 5x+8 3k (x+2) = 5x+6 3k = (5x+6) / (x+2) k = (5x+6) / (3x+6)

it is solved for k

and considering the condition for x<3:

3k (x+2) + 2 = 5x+8 3kx+6k=5x+6 (5-3k) x=6k-6 x = (6k-6) / (5-3k) x<3 ⇒ (6k-6) / (5-3k) <3 ⇒ 6k-6<15-9k ⇒ 15k<9 ⇒ k<9/15 ⇒ k<3/5

So,

k = (5x+6) / (3x+6) and k<3/5