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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