Question

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

Answer 1

The answer is:
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"  3 < x < 4 " ;    or;  write as:     "  4 > x > 3 " .
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Explanation:
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Given:
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" 4 < 2x + 10 < 18 "  ,
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Divide the entire inequality by "2" to simplify:
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{4 <  2x+10 < 18 } / 2  ;
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 2 < x+5 <9
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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
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Then we have;
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x + 5 < 9  ;

Subtract "5" from each side;

x + 5 - 5 < 9 - 5 ;

x < 4
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So, we have:

3 < x  and x  < 4
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We can combine these; and write as:
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                                "  3 < x < 4 " ;

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