## Precalculus (6th Edition) Blitzer

$$\frac{29}{30} \lt x \lt \frac{31}{30},$$ $$\frac{299}{300} \lt x \lt \frac{301}{300}$$
We solve the first part: $$|f(x)-5| \lt 0.1 \quad \Rightarrow \quad |3x+2-5| \lt 0.1 \quad \Rightarrow \quad 3|x-1| \lt 0.1 \quad \Rightarrow \quad |x-1| \lt \frac{1}{30} \quad \Rightarrow \quad -\frac{1}{30} \lt x-1 \lt \frac{1}{30} \quad \Rightarrow \quad \frac{29}{30} \lt x \lt \frac{31}{30}$$ Now, for the second part, we have: $$|f(x)-5| \lt 0.01 \quad \Rightarrow \quad |3x+2-5| \lt 0.01 \quad \Rightarrow \quad 3|x-1| \lt 0.01 \quad \Rightarrow \quad |x-1| \lt \frac{1}{300} \quad \Rightarrow \quad -\frac{1}{300} \lt x-1 \lt \frac{1}{300} \quad \Rightarrow \quad \frac{299}{300} \lt x \lt \frac{301}{300}$$