Answer:
the solution to the original inequality -8 < 3x + 1 ≤ 13 is -3 < x ≤ 4.
Explanation:
-8 < 3x + 1 .....(1)
3x + 1 ≤ 13 .....(2)
For inequality (1):
-8 < 3x + 1
To isolate 3x, we subtract 1 from both sides:
-8 - 1 < 3x
-9 < 3x
Dividing both sides by 3 (keeping in mind to reverse the inequality when dividing by a negative number):
-9/3 < 3x/3
-3 < x
So for inequality (1), we have x > -3.
For inequality (2):
3x + 1 ≤ 13
To isolate 3x, we subtract 1 from both sides:
3x ≤ 13 - 1
3x ≤ 12
Dividing both sides by 3:
(3x)/3 ≤ 12/3
x ≤ 4
So for inequality (2), we have x ≤ 4.
Combining the results:
We know x > -3 from inequality (1) and x ≤ 4 from inequality (2).
Therefore, the solution to the original inequality -8 < 3x + 1 ≤ 13 is -3 < x ≤ 4.