Help please - Solve each inequality?

Question

0 > 2(m - 5) > - 8

- 3 < 3 + 2w < 6

2 g/5 or 2g + 4 < - 6

also, find the largest possible values for a set of three consecutive even integers whose sum is less than 105.

Answer 1

0 &gt; 2(m - 5) &gt; - 8

=&gt; 0&gt;(m-5)&gt;-4

=&gt;5&gt;m&gt;1

- 3 &lt; 3 + 2w &lt; 6

=&gt; -6&lt;2w&lt;3

=&gt; -3&lt;w&lt;3/2

2g/5&lt; -6 =&gt;g&lt;-15

2g+4&lt;-6 =&gt;2g&lt;-10=&gt;g&lt;-5

So for 2 g/5 or 2g + 4 &lt; - 6 we require g&lt;-5

Suppose the first number is x, then the second is x+2 and the third x+4. We therefore want the highest even integer x such that:

x+(x+2)+(x+4)&lt;105

=&gt;3x&lt;99

=&gt;x&lt;33

Therefore the three numbers are 32,34,36.