What is the solution set for 4< 2x+10< 18

The answer is:

"  3 < x < 4 " ;    or;  write as:     "  4 > x > 3 " .

Explanation:

Given:

" 4 < 2x + 10 < 18 "  ,

Divide the entire inequality by "2" to simplify:

{4 <  2x+10 < 18 } / 2  ;

 2 < x+5 <9


First, we have:

2<x+5 ; 

Subtract "2" form each side:

(2-2) < (x + 5 - 2) ; 
 
0 < x - 3 ;
 
Add "3" to each side:

0 + 3 < x - 3 + 3 ;

3 < x

Then we have;

x + 5 < 9  ;

Subtract "5" from each side;

x + 5 - 5 < 9 - 5 ;

x < 4

So, we have:

3 < x  and x  < 4

We can combine these; and write as:

                                "  3 < x < 4 " ;

      or:  write as:     "  4 > x > 3 " .

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