# Find the value of b if b satisfies 3=< 2b-3 =< 13.

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We have 3=< 2b-3 =< 13. We have to solve this inequality to determine the values of b.

We start by adding 3 to all the terms

=> 3+3 =< 2b - 3 +3 =< 13 +3

=> 6=< 2b =< 16

Now we divide all the terms by 2

=> 6/2 =< 2b/2 =< 16/2

=> 3=< b =< 8

We can see that b is greater than or equal to 3 and less than or equal to 8.

**Therefore b has to lie in the set [ 3,8]**

Given the inequality 3=< 2b-3 =< 13.

We need to find all possible b values where the inequality holds.

Let us solve the same way we solve the equality.

==> 3 =< 2b-3 =< 13

The goal is to isolate b by itself in the middle of the inequality.

==> We will add 3 to all sides.

==> 3+ 3 =< 2b -3 + 3 =< 13 + 3

==> 6 =< 2b =< 16.

Now we will divide all terms by 2.

==> 6/2 =< 2b/2 =< 16/2

==> 3 =< b ==< 8.

Then we notice that b values are bounded by the numbers 3 and 8.

Then, b belongs to the interval [ 3, 8].

**==> b = [ 3, 8].**

We'll solve the double inequality, starting by the left side:

3=< 2b-3

We'll subtract 3 both sides:

3 - 3 =< 2b - 3 - 3

0=<2b - 6

We'll add 6 both sides:

2b>=6

b>=6/2

b>=3

We'll solve the right inequality:

2b-3 =< 13

We'll add 3:

2b =< 16

b =< 16/2

b =< 8

**The interval of admissible values for b is: [3 , 8].**