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Question

Solve the Inequality. Graph the solution, If possible. 23z+6+3>27-2|3 z+6|+3>27

Solution

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Given:\textbf{Given:}

23z+6+3>27-2\left|3z+6\right|+3>27

Subtract 33 from above inequality:

23z+6+33>273\Rightarrow -2\left|3z+6\right|+3-3>27-3

23z+6>24, divide by 2-2\left|3z+6\right|>24, \ \text{divide by} \ -2

The sign of inequality is also changed as inequality is divided by a negative number.

223z+6<242\Rightarrow \dfrac{-2}{-2}\left|3z+6\right|<\dfrac{24}{-2}

Simplifying the above inequality:

3z+6<12\Rightarrow \left|3z+6\right|<-12

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