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Answer 1 · 2017-09-17T14:07:49

#[- 3, 9)#

We have: #0 le frac(1)(3) x + 1 < 4#

Let's subtract #1# from the inequality:

#Rightarrow 0 - 1 le frac(1)(3) x + 1 - 1 < 4 - 1#

#Rightarrow - 1 le frac(1)(3) x < 3#

Then, let's multiply by #3#:

#Rightarrow - 1 times 3 le frac(1)(3) x times 3 < 3 times 3#

#therefore - 3 le x < 9#

Therefore, the solution interval to the inequality is #[- 3, 9)#.