Question 253323
<pre><font size = 4 color = "indigo"><b>
x = 1st integer
x+1 = 2nd integer
x+2 = 3rd integer
x+3 = 4th integer

{{{16< x + (x+1)+(x+2)+(x+3)<24}}}

{{{16< x + x+1+x+2+x+3<24}}}

{{{16<4x + 6<24}}}

Subtract 6 from all three sides

{{{10<4x<18}}}

Divide through by 4

{{{10/4<x<18/4}}}

{{{2.5<x<4.5}}}

The only two integers x between 2.5 and 4.5 are 3 and 4

So there are two sets:

x = 1st integer = 3
x+1 = 2nd integer = 4
x+2 = 3rd integer = 5
x+3 = 4th integer = 6
sum = 3+4+5+6=18

and

x = 1st integer = 4
x+1 = 2nd integer = 5
x+2 = 3rd integer = 6
x+3 = 4th integer = 7
sum = 4+5+6+7=22

Edwin</pre>