How do I solve -14<=-2x-2<=-8

This equation must be answered using interval notation , and I must show all work
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Divide interval expression through by 2: -7<=-x-1<=-4. Now add 1 throughout: -6<=-x<=-3. Take this as two inequalities: -6<=-x and -x<=-3. In the first inequality add 6 throughout and in the second add 3: 0<=6-x and 3-x<=0. Now add x through both inequalities: x<=6 and 3<=x. Combining these: 3<=x<=6.

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