Problem 37
We subtract 1 from all three parts to isolate the variable x.
-5 < x+1 < 4
-5-1 < x+1-1 < 4-1
-6 < x < 3 is the final answer
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Problem 40
Let's isolate the 3x portion first. To do this, we add 1 to all three sides.
2 < 3x-1 ≤ 6
2+1 < 3x-1+1 ≤ 6+1
3 < 3x ≤ 7
Then we divide all parts by 3 to fully isolate x.
3/3 < 3x/3 ≤ 7/3
1 < x ≤ 7/3 is the final answer