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# I need help to solve each inequality

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I need help to solve each inequality

6.   3| x - 3 | < 12

7.  5| 2x + 8 | + 4 < 9

8.  -2| 8x - 4 | + 1 < -15

Mar 26, 2019

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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

Mar 26, 2019