algebra... I don't get it... please help...?

Question

1.) -14 < 2j+ 3≤ 6

2.) -3 ≤-x- 5 ≤0

3.) -x+ 5 < 3x+ 1

Answer 1

You can easily solve completely without partitioning the problem. For example, consider -3 < -x - 5 <= 0 ; add 5 throughout to get 2 < -x <= 5 , and now multiply through by -1 to get -2 > x >= -5 .

Answer 2

For double inequalities like #1 and #2, it might help if you break it up into two separate inequalities, and do each one separately. For example, you can rewrite the first one as:

-14 < 2j + 3 ...and.. 2j+3 ≤ 6

Solve each of these separately for j, and combine the results at the end.