Posted by **Anonymous** on Wednesday, September 22, 2010 at 11:09pm.

Ex 3:

4x-7<2x+5

4x-7-2x<2x-2x+5

2x-7<5

2x-7+7<5+7

2x<12

2x/2<12/2

x< 6 Note I did not switch the order of the inequality here since I divided by a positive number. Multiplying or dividing by a positive number does not change the order of the inequality.

So x has to be less than or equal to 6. So 5 should work well and so should 6.

Check:

4(6)-7<2(6)+5

24-7<12+5

17<17

This is true since 17=17 so it looks like 6 is the correct cut off.

Check:

5 should work too.

4(5)-7<2(5)+5

20-7<10+5

13<15

This is also true so it looks like my answer is correct so the answer is {x|x < 6} which again is read "The set of all values for x such that x is less than or equal to 6.”

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