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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
 #1
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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

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