I need help to solve each inequality

6. $3| x - 3 | < 12$

First, divide both sides by $3$ to get $| x - 3 | < 4$. Now we have that $x - 3 < 4$ or that $x - 3 > -4$. By solving each one, we get $x<7$ or $x>-1$. This gives us $(-1, 7)$.

7. $5| 2x + 8 | + 4 < 9$

First, subtract $4$ from both sides to get $5\left|2x+8\right|<5$. Then, we can divide by $5$ on both sides to get $\left|2x+8\right|<1$. Now, we have $-1<2x+8<1$. By subtracting $8$ on both sides then dividing by $2$, we get $x>-\frac{9}{2}$ and $x<-\frac{7}{2}$ so we have $(-\frac{9}{2},-\frac{7}{2})$.

8. $-2| 8x - 4 | + 1 < -15$

Subtract $1$ from both sides to get $-2\left|8x-4\right|<-16$. Then, divide by $-2$ on both sides to get $\left|8x-4\right|>8$. Now, we can get that $8x-4>8$ and $8x-4<-8$. By simplifying both inequalities, we get $\:\left(-\infty \:,\:-\frac{1}{2}\right)\cup \left(\frac{3}{2},\:\infty \:\right)$. 

- Daisy