2<2x-6<8

Add 6 to each section of the inequality because it does not contain the variable we are trying to solve for.

2+6<2x<8+6

Add 2 and 6.

8<2x<8+6

Add 8 and 6.

8<2x<14

8<2x<14

Divide each term in the inequality by 2.

82<2×2<142

Divide 8 by 2.

4<2×2<142

Cancel the common factor.

4<2×2<142

Divide x by 1.

4<x<142

4<x<142

Divide 14 by 2.

4<x<7

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