Solve the following inequality. Express your answer in interval notation. `2<=-(-1/2x-3)<6` 

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lfryerda eNotes educator| Certified Educator

If you have more than one question, you need to make separate posts.

To solve the inequality, we need to separate this into two separate inequalities, and then solve each of them.  

The first is:

`2<=-(-1/2x-3)`   distribute negative

`2<=1/2x+3`   move 3 to other side

`-1<=1/2x`   multiply by 2

`-1<=x`   read from right to left instead of left to right


The other inequality is:

`-(-1/2x-3)<6`   distribute negative

`1/2x+3<6`   move 3 to other side

`1/2x<3`   multiply by 2


The solution to the original inequality is the combination of the two separate ones, which is `-1<=x<6`  which is `x in[-1,6)` in interval notation.

The solution is `x in[-1,6)` .