solve the inequality 7 =< 2x-5 =< 11

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Given the inequality:

7 =< 2x-5 =< 11

We need to find the values of x that verifies the inequality.

First we need to isolate x in the middle by itself.

We will add 5 to all sides.

==> 7+5 =< 2x =< 11+5

==> 12 =< 2x =< 16

Now we will divide by 2.

==> 12/2 =< x =< 16/2

==> 6 =< x =< 8

Then the values of x that verifies the inequality is bounded by 6 and 8.

**Then x belongs to the interval [6, 8].**

We have to solve the inequality 7 =< 2x-5 =< 11

7 =< 2x-5 =< 11

7 =< 2x-5

=> 7 + 5 =<2x

=> 12 =< 2x

=> 6 =<x

2x-5 =< 11

=> 2x =< 16

=> x =< 8

**The required values of x lie in [6, 8]**

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